PRACTICAL 
PHYSICAL  CHEMISTRY 

J.B.  FIRTH 


GIFT   OF 
MICHAEL  REESE 


PRACTICAL 
PHYSICAL    CHEMISTRY 


PRACTICAL 
PHYSICAL  CHEMISTRY 


BY 

JAMES   BRIERLEY   FIRTH 

(M.Sc.  MANGH.) 

LATE  DALTON  CHEMICAL  SCHOLAR,   MANCHESTER  UNIVERSITY 

ASSISTANT    LECTURER   AND   DEMONSTRATOR   IN  CHEMISTRY,    ARMSTRONG 

COLLEGE,   NEWCASTLE-ON-TYNE 


WITH    SEVENTY-FOUR    DIAGRAMS 


NEW   YORK 

D.   VAN    NOSTRAND    COMPANY 

25    PARK    PLAGE 

1916 


Printed  in  England 


PREFACE 

DURING  recent  years  it  has  come  to  be  more  widely 
recognized  in  the  various  schools  of  chemistry  that  a 
study  of  physical  chemistry  is  necessary  for  all  those  who 
wish  to  study  chemistry  with  any  degree  of  thoroughness. 

The  theoretical  significance  of  physico-chemical  constants, 
and  the  fact  that  they  find  their  application  in  almost  every 
branch  of  chemistry,  renders  it  essential  for  all  students  of  the 
science  to  become  familiar — to  some  extent,  at  any  rate — with 
physico-chemical  methods. 

It  is  not  possible  within  the  limits  of  a  small  volume  such 
as  this  to  deal  with  every  phase  of  the  subject.  I  have, 
therefore,  chosen  such  experiments  as  will  demonstrate  the 
fundamentals  of  the  subject,  in  order  that,  in  the  first  place, 
the  student  may  familiarize  himself  with  physico-chemical 
measurements,  and  secondly,  that  he  may  fix  more  firmly  in 
his  memory  the  knowledge  that  he  has  already  gained  in  the 
lecture  theatre.  If  a  science  is  to  really  live,  it  is  essential 
that  theory  and  practice  should  go  hand  in  hand.  One 
principle  demonstrated  by  the  student  himself  is  of  far  more 
value  to  the  student  than  pages  of  lecture  notes. 

The  importance  of  spectrum  analysis  seems  to  have  been 
overlooked  in  the  past,  but  it  is  the  opinion  of  the  author 
that  the  student  should  at  least  be  familiar  with  the  principal 
features  of  the  subject,  such  as  "  mapping  of  spectra "  and 
"  determination  of  wave-lengths,"  etc.  ;  therefore  a  short 
chapter  on  this  subject  finds  a  place  in  the  present  volume. 

Short  chapters  of  Electrochemical  Analysis,  Electrolytic 
Preparations,  have  also  been  included,  because,  besides  their 
purely  academic  value,  they  have  their  industrial  applications. 


vi  PRACTICAL  PHYSICAL  CHEMISTRY 

I  have  thought  it  necessary,  in  certain  sections  at  any  rate, 
to  introduce  just  sufficient  theory  to  enable  the  student  to 
understand  the  principles  of  his  experiment,  because,  owing 
to  the  fact  that  many  experiments  require  special  apparatus, 
it  is  not  possible  for  all  the  students  to  do  the  same  experi- 
ment at  the  same  time,  and  it  frequently  happens  that  a 
student's  practical  work  is  in  advance  of  his  theory.  Hence 
the  introduction  of  a  little  theory  prevents  the  experiment 
becoming  mechanical. 

It  will  not  be  usually  possible  for  students  to  perform  ex- 
periments in  all  the  sections,  nor  is  it  possible  to  say  what 
sections  should  be  omitted  where  the  time  is  limited,  because 
so  much  will  depend  upon  the  particular  requirements  of  the 
student.  For  example,  it  may  seem  advisable  for  a  student 
who  intends  to  pursue  certain  industrial  work  to  study 
thoroughly  electro-analysis,  electrolytic  preparations,  etc.,  at 
the  expense  of  some  of  the  more  academic  sections.  Therefore, 
the  actual  experiments  selected  must  be  left  to  the  discretion 
of  the  demonstrator. 

In  every  case  the  student  should  read  up  the  corresponding 
section  in  some  theoretical  textbook  as  soon  as  possible. 
Senter's  "  Outlines  of  Physical  Chemistry  "  admirably  meets 
the  requirements  of  most  students. 

A  slight  knowledge  of  advanced  mathematics  (elements  of 
calculus,  etc.)  has  been  assumed. 

It  is  not  possible  to  acknowledge  all  the  textbooks  which 
have  assisted  in  compiling  the  present  volume,  but,  in  con- 
clusion, I  should  like  to  acknowledge  my  indebtedness  to 
Ostwald-Luther's  "Physical  Chemistry  Measurements," 
Traube's  "  Physicochemical  Methods,"  Elbs'  "Electrolytic 
Preparations,"  Watts'  "  Spectroscopy." 

J.  B.  F. 

CHEMICAL  DEPARTMENT 

ARMSTRONG  COLLEGE 

NEWCASTLE-ON-TYNE 
January ',  1915 


CONTENTS 

CHAPTKR  PAGE 

INTRODUCTION  ix 

I.   THERMOSTATS  1 

II.   DENSITY   OF  GASES,   LIQUIDS,   AND  VAPOURS  6 

III.  DETERMINATION     OF     VISCOSITY    AND     SURFACE 

TENSION  -         15 

IV.  DETERMINATION   OF  SOLUBILITY-  21 
V.   DETERMINATION   OF   MOLECULAR   WEIGHTS  -         23 

VI.    DETERMINATION   OF  TRANSITION   POINTS  -         35 

VII.    OSMOTIC  PRESSURE  41 

VIII.   REFRACTIVITY   MEASUREMENTS    -  46 

IX.    ROTATION   OF  THE   PLANE  OF   POLARIZATION  -         55 

X.    SPECTRUM   ANALYSIS         -  62 

XI.   DETERMINATION   OF   PARTITION   COEFFICIENTS  71 

XII.   THERMO-CHEMICAL  MEASUREMENTS  74 

XIII.    DETERMINATION    OF  TRANSPORT   NUMBERS  87 

XIV.   ELECTRICAL   CONDUCTIVITY  91 

XV.    ELECTROMOTIVE   FORCE  -  107 

XVI.    VELOCITY   OF  CHEMICAL   REACTION  -      137 

XVII.   QUANTITATIVE   ELECTROLYTIC   DETERMINATIONS-      144 

XVIII.   ELECTROLYTIC   PREPARATIONS       -  -      151 

XIX.    PREPARATION   OF  COLLOIDS  -      158 

APPENDIX  163 
INDEX     ------      176 


VII 


INTRODUCTION 

The  Balance :  Rules  for  Weighing — The  balance  should  be 
placed  so  that  it  is  protected  from  direct  rays  of  the  sun  or 
other  sources  of  heat,  which  would  produce  inequality  of  tem- 
perature in  the  different  parts.  It  should  rest  on  a  firm 
bench,  which  is  free  from  vibration. 

The  balance  must  be  kept  horizontal  by  means  of  the  foot 
screws.  This  position  is  indicated  by  a  spirit-level  or  plumb-line. 

The  interior  of  the  balance  case  should  be  kept  dry  by 
means  of  calcium  chloride,  etc. 

The  weights  should  be  placed  on  the  pan  only  after  the 
arrestment  of  the  beam,  picking  up  the  weights  in  all  cases  by 
means  of  forceps.  Rapid  swinging  of  the  beam  is  not  con- 
ducive to  accurate  weighing,  and  the  final  weighings  should 
be  made  with  the  case  closed. 

Adjustment  of  the  Balance — The  sensibility,  and  hence  the 
period  of  vibration,  are  regulated  by  means  of  a  gravity  bob, 
situated  near  the  middle  of  the  pointer.  The  adjustment  is  so 
made  that  the  period  of  vibration  for  a  short-armed  balance  is 
from  six  to  ten  seconds,  and  from  ten  to  fifteen  seconds  for  a 
long-armed  balance. 

The  adjustment,  so  that  the  pointer  swings  equally  on  both 
sides  of  the  middle  division  of  the  scale,  is  made  by  movable 
weights  attached  to  the  end  of  the  beam ;  when  these  fail,  the 
unsymmetrical  weight  in  the  middle  of  the  beam  is  given  such 
a  position  that  the  adjustment  can  be  made. 

Determination  of  the  Zero-Point — It  is  not  necessary  nor 
desirable  in  weighing  that  the  weights  be  so  adjusted,  so  that 
the  pointer  will  swing  equal  on  both  sides  of  the  middle 


x  PRACTICAL  PHYSICAL  CHEMISTRY 

division  of  the  scale.  The  actual  resting-point  is  determined 
from  the  several  turning-points  of  the  pointer. 

The  zero  is  determined  by  releasing  the  beam  and  allowing 
it  to  swing  freely  (free  from  any  load).  Then,  neglecting  the 
first  swing,  observe  the  extreme  points  on  the  scale,  taking 
two  readings  on  one  side,  and  one  on  the  other.  Suppose  the 
readings  on  the  right  are  called  positive,  and  those  on  the  left 
negative,  and  the  readings  on  the  right  were  -t-6'5  and  +5*6, 
and  the  reading  on  the  left  —  5 '8,  then  the  mean  reading  on 
the  right  was  +6-01,  and  the  zero  will  be  halfway  between 
+  6-01  and  -5'8— i.e.,  +0-10,  that  is,  (H  of  a  division  to  the 
right.  It  frequently  happens  that  this  zero  changes  after 
the  weighing  of  heavy  loads,  therefore  it  must  be  frequently 
redetermined. 

As  before  mentioned,  it  is  not  desirable  to  have  to  adjust 
the  weights  so  that  the  pointer  moves  "  symmetrically " 
about  this  zero ;  such  a  process  would  be  tedious,  and  is 
absolutely  unnecessary.  To  avoid  this  the  sensibility  of  the 
balance  is  determined.  By  the  sensibility  of  a  balance  is 
meant  the  change  of  position  of  the  zero,  for  an  increase  of 
1  mgm.  on  one  side  of  the  balance. 

The  weighing  on  the  pan  is  only  made  to  within  1  cgm., 
the  milligrams  being  determined  by  means  of  a  rider  working 
on  a  graduated  beam.  Suppose,  when  the  weight  has  been 
practically  determined,  the  resting-point  calculated  from  the 
swings  is  2'40.  Now  move  the  rider  so  as  to  increase  the 
weights  by,  say,  2  mgms.,  and  the  resting-point  now  be  — 1*8. 
The  resting-point  has  moved  through  4*2  divisions  for  a 
change  of  2  mgms. — i.e.,  2*1  divisions  for  1  mgm.  This  is  the 
sensibility  of  the  balance  for  the  load  used.  The  sensibility 
changes,  however,  with  the  load,  and  it  is  therefore  necessary 
to  determine  the  sensibility  for  different  loads,  say  for  every 
10  grams.  Then  plot  a  curve  so  that  the  sensibility  can  be 
determined  for  any  load  ;  plot  the  loads  as  abscessse  and  the 
corresponding  sensibilities  as  ordinates. 


INTRODUCTION  xi 

Knowing  the  sensibility  of  the  balance,  it  is  possible  to 
weigh  to  the  fourth  decimal  place.  Suppose  the  zero  of  a 
balance  is  found  to  be  +  1,  and  that  in  a  certain  weighing  the 
resting-point  is  found  to  be  +1*5,  also  let  the  sensibility  for  this 
particular  load  be  3-5.  In  the  weighing  we  have  a  change  of 
resting-point  of  +  0*5.  Now,  we  know  from  the  sensibility  that 
1  mgm.  produces  a  change  of  3  '5,  hence  a  change  of  0*5  is 

0*5 
produced  by    —  =0-14   mgms.      Thus,  if  the  weights  plus 

o'O 

rider  on  the  balance  read  21-693  grams,  the  true  weight  is 
21'69314  grams.  It  is  usual  to  take  the  nearest  fourth  decimal 
place,  as  without  additional  precautions  the  fifth  place  is  of  no 
value. 

Calibration  of  a  Set  oj  Weights  —  Let  the  larger  set  of  weights 
be  designated  50',  2(X,  KX,  10*,  5',  2',  1',  1",  1'". 

Place  the  50-gram  weight  on  the  left-hand  pan  and  exactly 
balance  it  by  the  others,  the  final  adjustment  being  done  by 
the  method  of  oscillation.  Then  place  the  50-grain  weight 
on  the  right-hand  pan,  and  repeat  the  weighing.  Suppose 

we  have  — 

Left.  Right. 

(1)  50'  20'+  10'  +  10"  +  -  +  .  .-ha,  mg. 

(2)  20'  +  10'  +  10"+  .  .  +  b,  mg.  50' 

then          50'  =  20'  +  10'  +  10"+   .  .   +\(a  +  l)mg. 
Similarly  we  obtain  — 


and  so  on. 

Putting  a,  /3,  y,  .  .  .  for  J(a  +  b),  J(c  +  d),  \(e  +/)  respectively, 
we  get- 

507  =20'+  !(/+  10"+  .  .  .   +a 

20'  =  10'  +  10"  +J3 

10"=1(X  +  y 

5'  +  2'  +  l'  +  r+l"'  =  10'  +8 

in  which  a,  (3,  y,  8,  can  be  either  positive  or  negative. 


xii  PRACTICAL  PHYSICAL  CHEMISTRY 

Then,  comparing  all  weights  against  the  10' -grain  weight, 
we  have — 


10"=  1x10'  +  7 
10'  =  10' 


_ 
S  =  50'  +  20'  +  10'  +  10"  +  5'  +  2'  +  1'  +  1"  +  1'"  = 


Let  TV  (a  +  2/2  +  4y  +  28)  =  o-,  then 
10'    =  10  grams  -o- 
10*  =  10  grams  =  o-  +  y 
5'  +  2'  +  1'  +  1*  +  1"'=  10  grams  -  a-  +  8 

20'   =20  grams  -2<r  +  (3  +  y 
50'   =50 


The  actual  values  of  a,  /3,  y,  etc.,  have  been  determined 
during  the  weighing,  and  can  here  be  substituted  in  the 
above. 

In  a  similar  manner  the  5',  2',  1',  1",  V"  are  compared  with 
each  other,  and  also  the  fractional  weights.  From  the  values 
thus  obtained  a  table  showing  the  exact  value  of  each  weight 
should  be  made. 


PRACTICAL  PHYSICAL  CHEMISTRY 

CHAPTEE  I 
THERMOSTATS 

IN  order  to  perform  many  of  the  experiments  described 
in  the  present  volume,  it  is  necessary  that  the  whole  of 
the  materials  used  should  remain  at  a  constant  and  definite 
temperature  throughout  the  duration  of  the  experiment. 
This  is  usually  accomplished  by  immersing  the  apparatus 
and  its  contents,  or  such  portions  as  may  be  necessary, 
in  a  bath  usually  of  water,  the  heating  (or  cooling)  of  which 
can  be  so  automatically  controlled  so  that  the  temperature 
remains  constant  within  certain  narrow  limits  for  an  indefinite 
period,  or  at  any  rate  for  the  duration  of  any  experiment. 
A  bath  which  is  so  regulated  is  known  as  a  thermostat. 

The  nature  of  the  bath  may  vary  according  to  the  require- 
ments of  the  experiment.  In  some  cases  a  large-sized  beaker 
will  suffice,  but  usually  a  sheet  copper  (or  galvanized  iron) 
tank,  about  60  cms.  x  60  cms.  x  60  cms.,  is  used.  Very  often 
a  cylindrical  bath  of  similar  dimensions  is  used  instead  of  a 
cubical  bath.  In  cases  where  it  is  necessary  to  observe  the 
apparatus  during  an  experiment,  a  thermostat  in  which  a 
sheet  of  glass  has  been  let  in  on  opposite  sides  is  used.  But 
very  often  for  such  experiments  a  large  beaker  or  an  inverted 
bell  jar  may  be  conveniently  substituted.  The  copper  or  iron 
bath  should  be  covered  on  the  outside  with  a  layer  of  felt. 

Thermo-Regulators — The  heating  of  the  bath  is  usually 
effected  by  means  of  a  gas  flame.  But  it  is  obvious  that  once 
the  bath  has  attained  the  required  temperature,  the  function 
of  the  flame  is  to  counterbalance  all  loss  of  heat  from  such 
causes  as  radiation,  evaporation,  etc.,  which  is  by  no  means 
a  constant  factor.  Hence  it  is  necessary  to  automatically 
1 


.*  :  .  THERMOSTATS 


control,  t'%me.;.  ihis  is  done  by  means  of  a  thermo-regulator  . 
Two  'useful  types  aru  shovrn  in  Fig.  1.  The  bulb  portion  A  is 
filled  with  some  liquid  which  has  a  high  coefficient  of  expan- 
sion, and  at  the  same  time  a  fairly  high  boiling-point. 
Toluene  is  very  suitable  for  the  purpose.  The  rest  of  the 
apparatus  is  filled  with  mercury  up  to  tube  JB,  which  is  of 
small  bore,  in  order  to  increase  the  sensitiveness  of  the  regu- 
lator. The  gas  passes  in  through  tube  (7,  which  is  fixed  to 


FIG.  1 

the  top  of  the  regulator  tube  by  a  cork,  and  thence  through 
E  to  the  burner.  If  the  temperature  of  the  bath  gets  too 
high,  the  toluene  expands,  drives  the  mercury  up  the  tube  J5, 
and  closes  the  inlet  tube  (7,  thus  cutting  off  the  gas-supply. 
To  prevent  the  flame  being  extinguished,  a  certain  amount  of 
gas  passes  to  the  burner  by  means  of  the  by-pass  D,  the 
actual  amount  of  gas  passing  being  controlled  by  a  stop-cock 
or  clip,  and  it  is  arranged  that  the  desired  temperature  is 
almost  maintained  when  C  is  closed. 


TO  FILL  AND  ADJUST  THE  REGULATOR  3 

To  fill  and  adjust  the  Regulator — Eemove  tube  (7  and  fit  a 
glass  tube  H ;  connect  this  by  means  of  rubber  tubing  (pres- 
sure tubing),  provided  with  a  pinch-cock,  F,  to  a  pump. 
Connect  a  short  length  of  glass  tubing  to  Et  provided  also 
with  a  pinch-cock.  The  glass  tube  dips  into  a  beaker  of 
toluene  (see  Fig.  2).  Now  close  the  pinch-cock  at  G  and 
exhaust  the  apparatus  by  means  of  the  pump ;  then  close  the 
pinch-cock  F  and  open  the  pinch-cock  on  G,  when  toluene  will 


FIG.  2 

be  drawn  into  the  apparatus.  Now  invert  the  regulator  and 
again  exhaust,  and  again  admit  toluene  until  only  a  small 
amount  of  air  remains.  Again  exhaust  and  pour  over  the 
bulb  of  the  regulator  a  stream  of  hot  water,  causing  the  toluene 
to  vaporize,  thus  driving  out  most  of  the  air ;  shut  off  the 
pump,  and  again  admit  toluene  whilst  cooling.  There  should 
still  be  left  a  small  air  space.  Now  remove  the  tube  at  H 
and  introduce  a  quantity  of  mercury.  Again  invert  the 
regulator  so  that  the  mercury  resides  round  the  tube  H  (see 
Fig.  2).  Now  exhaust  while  heating  the  bulb  with  hot  water 
until  all  the  air  has  been  driven  out.  Now  invert  the  regu- 


THERMOSTATS 


lator,  and  on  cooling  the  mercury  will  be  drawn  into  the  stem 
of  the  regulator.  If  a  small  bubble  of  air  still  persists,  it  can 
frequently  be  got  rid  of  by  slight  shaking,  and  then  allowing 
to  stand,  since  toluene  dissolves  air  to  some  extent.  The 
excess  of  toluene  which  appears  on  the  top  of  the  mercury 
may  be  removed  by  a  small  roll  of  filter-paper.  To  adjust 
the  quantity  of  mercury,  place  the  regulator  in  a  bath  at  the 
desired  temperature.  Then  remove  the  mercury  by  means  of 
a  pipette  (see  Fig.  3)  until  the  meniscus  is  just  above  the  top 
of  the  capillary.  If  insufficient  mercury  has  been  added,  heat 


FIG.  3 


FIG.  4 


up  the  bath  until  the  mercury  appears  above  the  capillary, 
then  add  a  little  more,  setting  the  regulator  as  before.  The 
tube  C  is  then  put  in  position,  so  that  at  the  temperature 
required  it  is  just  closed  by  the  mercury.  This  position  has 
usually  to  be  found  by  trial.  This  regulator,  when  working 
properly,  should  be  given  a  constant  temperature  with  ±0*1  °. 
For  temperatures  below  that  of  the  surroundings,  a  regulator 
as  shown  in  Fig.  4  is  used.  It  is  filled  just  as  in  the  case 
of  the  gas  regulator.  The  adjustment  of  the  mercury 
meniscus  is  made  in  this  case  by  means  of  screw  H.  A  slow 


TO  FILL  AND  ADJUST  THE  REGULATOR  5 

stream  of  ice-cooled  water  is  admitted  at  L,  and  when  the 
bath  is  below  the  desired  temperature,  the  mercury  in  B  falls, 
thus  allowing  the  ice-cooled  water  to  escape  through  G  to 
waste.  As  the  temperature  rises  the  tube  G  is  closed  by  the 
mercury,  thus  causing  the  iced  water  to  escape  through  K, 
which  runs  into  the  bath.  The  rate  at  which  the  water 
enters  through  L  must  be  so  regulated  that  it  can  easily 
be  carried  away  by  tube  G  without  any  fear  of  it  rising  to 
the  level  of  K.  Owing  to  the  gradual  increase  in  the  amount 
of  water  in  the  thermostat,  the  bath  in  this  case  must  be  pro- 
vided with  an  overflow  tube,  which  is  connected  with  the 
sink. 

In  order  to  maintain  a  uniform  temperature  throughout 
the  bath  it  is  necessary  to  stir  the  water.  This  may  be  con- 
veniently done  by  means  of  an  air  blast  where  the  tempera- 
ture of  the  bath  is  not  too  high.  A  piece  of  soft  metal 
composition  tubing,  closed  at  one  end,  is  bent  in  the  form  of 
a  ring,  and  pierced  at  intervals  of  about  a  decimetre  with 
small  pinholes ;  this  is  connected  with  an  air  blast  such  as  is 
produced  by  a  water-blower.  As  the  air  escapes  it  stirs  up 
the  water.  Where  this  is  not  possible,  an  ordinary  stirrer 
may  be  used,  to  which  a  pulley  and  bearing  is  fitted.  A  con- 
venient stirrer  may  be  made  from  a  bicycle  hub,  by  replacing 
the  axle  by  a  longer  steel  rod,  on  one  end  of  which  is  attached 
a  screw  clip,  and  on  the  other  a  pulley.  A  suitable  form  of 
stirrer  can  be  fastened  on  by  the  screw  clip,  and  the  stirrer 
rotated  by  means  of  a  small  motor  or  hot  air  engine. 

The  thermo -regulator,  the  stirrer,  and  also  a  Beckmann 
thermometer,  are  supported  within  the  bath  by  means  of 
retort  clamps  fastened  to  the  side.  The  regulator  is  then 
connected  up  with  the  gas-supply  and  with  a  small  burner 
underneath  the  bath.  For  temperatures  below  50°  F.  a  suit- 
able burner  is  obtained  by  removing  the  tube  from  an 
ordinary  bunsen  burner.  For  higher  temperatures  a  bunsen 
fitted  with  a  rose  or  gauze  top  may  be  used.  The  bath 
should  initially  be  filled  with  water  which  has  been  heated  to 
approximately  the  temperature  required.  For  temperatures 
above  50°  F.  the  water  may  be  covered  with  a  layer  of  oil,  to 
prevent  undue  loss  by  evaporation. 

For  very  high  or  very  low  temperatures,  where  constancy  is 
required,  the  boiling-point  of  certain  liquids  is  used,  or  the 
melting  of  certain  solids.  For  suitable  substances  see  Appendix. 


CHAPTER  II 


DENSITY  OF  GASES,  LIQUIDS,  AND  VAPOURS 

Density  of  Gases  and  Vapours — Strictly,  the  density  of  a  gas 
is  the  mass  of  unit  volume — i.e.,  of  1  c.c. ;  but  as  gases  are 
greatly  influenced  by  temperature  and  pressure,  density  is 
defined  as  the  mass  of  unit  volume  at  N.T.P.  It  is,  however, 
more  convenient  to  determine  the  density  of  the  gas  relative 
to  some  standard  whose  density  is  taken  as  unity  when 
measured  under  the  same  temperature  and  pressure.  Hydro- 
gen is  frequently  taken  as  the  standard,  but  of  late  years 
oxygen  =  32  has  been  suggested,  since  in  chemistry  the 
densities  of  gases  are  usually  determined  with  a  view  to  ascer- 
taining their  molecular  weight;  and  as  oxygen  is  now  the 
standard  for  atomic  weights,  it  is  advisable 
to  determine  densities  by  this  standard  also. 

To  Determine  the  Absolute  Density  of  Dry 
Oxygen — A  clean  dry  bulb  about  200  c.c. 
capacity,  and  fitted  with  a  capillary  tube  and 
tap  (see  Fig.  5),  is  first  calibrated  by  weighing 
it  vacuous  and  then  filled  with  water  at  a 
known  temperature ;  then,  by  multiplying  the 
weight  of  water  by  its  density  at  that  particular 
temperature,  the  volume  of  the  bulb  can  be 
ascertained.  (Note — in  all  weighing  it  is  ad- 
visable to  use  a  counterpoise  of  approximately 
the  same  weight  and  volume  in  order  to 
eliminate  errors  due  to  the  buoyancy  of  the 
air.)  Having  determined  the  volume  of  the 
bulb,  it  is  now  dried  thoroughly  and  evacuated. 
Oxygen  dried  by  passing  through  calcium  chloride  tubes  is 
carefully  admitted,  the  bulb  being  placed  in  a  thermostat 


FIG.  5 


DENSITY  OF  GASES  AND  VAPOURS  7 

during  filling  (Fig.  6),  which  should  take  at  least  five  minutes, 
and  the  bulb  again  weighed. 


To  Pump 


FIG.  6 


If  w  is  the  weight  of  vacuous  bulb  and  W  the  weight  when 
full  of  oxygen,  then  W  -  w  =  weight  of  the  oxygen. 
If  V  =  tolume  of  the  bulb,  then— 


"(273  +  0x760* 

Hence  the  density  of  the  gas  will  be — 

_W-w 
V0    ' 

Since   1    gram   molecule    of   a  gas   occupies   22400   c.c.  at 
N.T.P.,  the  molecular  weight  will  be — 


M  =  22400  x 


(W-w) 


To  Determine  the  Density  of  Carbon  Dioxide  Relative  to 
Oxygen — Repeat  the  above  experiment,  weighing  the  bulb  this 
time  full  of  carbon  dioxide.  If  the  carbon  dioxide  is  generated 
in  a  Kipp's  apparatus,  the  bulb  is  filled  under  slight  pressure ; 
it  is  therefore  necessary  to  open  the  tap  for  a  second  to  allow 
the  gas  to  come  to  atmospheric  pressure. 

In  both  the  above  experiments  the  bulb  should  be  placed 


8         DENSITY  OF  GASES,  LIQUIDS,  AND  VAPOURS 

in  a  thermostat  during  the  filling,  and  should  remain  in  at 
least  five  minutes  before  closing  the  tap. 

Since  the  volume,  temperature,  and  pressure,  are  the  same 
for  both  gases,  the  relative  density  will  be — 

Weight  of  C02 
Weight  of  0,' 

Determination  of  Vapour  Density  (Victor  Meyer's  Method)— 
The  commonest  and  most  convenient  method  for  the  deter- 
mination of  the  density  of  the  vapour  of  a  substance  which 
is  not  a  gas  at  ordinary  temperatures  is  that  due  to  Victor 
Meyer. 

A  definite  quantity  of  substance  is  introduced  into  an  air 
chamber,  which  is  kept  at  a  constant  temperature  (this 
temperature  must  be  higher  than  the  boiling-point  of  the 
substance  to  be  tested).  When  the  substance  vaporizes  it 
displaces  its  own  volume  of  air,  which  is  collected  and 
measured  at  a  known  temperature  and  pressure  (usually  air 
temperature). 

The  apparatus  (Fig.  7)  consists  of  a  cylindrical  glass  vessel, 
having  near  the  top  two  side  tubes,  and  closed  with  a  rubber 
stopper  lubricated  with  graphite.  Through  side  tube  A  is 
fitted,  by  means  of  a  rubber  stopper,  a  short  glass  rod  flattened 
at  the  end.  Side  tube  J5,  through  which  the  expelled  air 
passes,  leads  into  an  inverted  graduated  glass  cylinder  over 
water  (boiled).  This  glass  vessel  is  surrounded  by  an  outer 
jacket,  in  which  some  suitable  liquid  is  boiled. 

Details — Weigh  out  into  a  small  stoppered  tube  or  bulb  a 
small  quantity  of  the  substance  (e.g.,  chloroform).  Heat  up 
the  tube  C  with  the  vapour  of  some  suitable  liquid,  until 
no  more  air  is  expelled  from  tube  B.  Then  introduce  the 
weighed  substance  through  the  top  of  the  tube,  so  that 
it  rests  on  the  flattened  part  of  the  glass  rod ;  see  that  all 
joints  are  tight ;  invert  a  graduated  tube  filled  with  water 
over  the  side  tube,  and  then  slightly  twist  the  glass  rod  so 
that  the  tube  falls  to  the  bottom.  (Note — the  bottom  should 
be  protected  with  a  wad  of  asbestos  fibre.)  Vaporization 
takes  place,  and  equivalent  volume  of  air  is  expelled.  When 
no  further  air  is  expelled,  the  volume  in  the  graduated  tube 
is  read  off. 


DENSITY  OF  GASES  AND  VAPOURS 


9 


Cakulation—Let  V  be  the  volume  of  air  expelled, 
t  the  temperature  of  the  air, 
p  the  barometric  pressure, 
x  the  vapour  pressure  of  water  vapour  at  <°C, 
w  the  weight  of  substance  taken, 
h  pressure    due    to    column   of    water    in 
graduated  tube. 


FIG.  7 


10        DENSITY  OF  GASES,  LIQUIDS,  AND  VAPOURS 

The  volume  of  air  at  N.T.P.— 

Vx273x(j?-a;-fr) 
°~      (£  +  273)  x  760     ' 

Hence  we  get  V0,  which  is  the  volume  which  w  grams  of  the 
substance  would  have  if  it  were  a  vapour  at  N.T.P. 

w 
.*.  Weight  of  1  c.c.  of  vapour  =  y-« 

•  o 

W 

And  the  molecular  weight  =  22400  x  y-. 

The  density  relative  to  some  standard  is  found  by  dividing 

the  weight  of  1  c.c.  of  vapour  by  the  weight  of  1  c.c.  of  unit 

of  gas  (usually  air  or  hydrogen). 

Suitable  heating  substances  are  water,  100° ;  aniline,  183° ; 

nitrobenzene,  211°  ;  diphenylamine,  300°  ;  paraffin  bath,  350°; 

sulphur,  448°  C. 

The  heating  liquid  should  have  a  boiling-point  about  30°  to 

40°  above  the  vaporizing-point  of  the  substance. 

Density  of  Liquids — The  density  of  a  liquid  is  the  mass  of 

unit  volume.     For  liquids  the  mass  of  1  c.c.  of  water  at  4°  C. 

is  taken  as  the  unit  of  mass. 
Hence  the  density  of  a  liquid 
may  be  defined  as  the  ratio  of 
its  mass  to  the  mass  of  an 
equal  volume  of  water  at  4°  C. 
The  most  convenient  form  of 
apparatus  for  determining  the 
density  of  liquids  is  what  is 
known  as  a  "  pyknometer " 
(Fig.  8).  It  consists  essentially 
of  a  U  tube  ;  usually  one  limb 
is  about  1-5  cms.  diameter,  and 
the  other  capillary  1  to  1'5  mm. 
bore.  For  accurate  experiments 
the  two  ends  of  the  tube  are 
fitted  with  ground  glass  caps. 

For  ordinary  purposes  these  may  be  omitted,  except  where 

very  volatile  liquids  are  used. 

Prior  to  making  a  determination  of  the  density  of  a  liquid, 

the   pyknometer   should   be  thoroughly  cleaned  and  dried. 

This  may  be  conveniently  done  by  washing  successively  with 


FIG.  8 


DENSITY  OF  LIQUIDS  11 

distilled  water,  alcohol,  and  ether,  and  finally  drawing  a 
current  of  dry  air  through  the  tube.  Heating  the  tube  should 
be  avoided,  as  it  takes  the  tube  some  time  to  recover  its 
normal  volume  after  heating  (from  ten  hours  to  several  days). 

The  pyknometer  is  then  weighed  by  suspending  it  from  the 
beam  of  the  balance  with  a  double  hook  of  platinum  wire  ; 
then  fill  the  pyknometer  with  cold,  freshly  distilled  water. 
This  is  conveniently  done  by  attaching  a  rubber  tube  to  the 
capillary  tube  and  placing  the  other  end  in  the  distilled  water 
and  sucking  gently. 

The  pyknometer  is  then  suspended  in  a  thermostat,  so  that 
the  two  ends  are  just  about  2  cms.  above  the  lerel  of  the 
water  in  the  thermostat. 

When  the  water  in  the  pyknometer  has  attained  the  tem- 
perature of  the  thermostat  (about  20  mins.),  the  amount  of 
water  must  be  so  adjusted  that  it  fills  the  pyknometer  to  a 
definite  mark  on  the  capillary  tube.  If  it  is  necessary  to 
introduce  a  little  water,  this  may  be  done  by  placing  a  tube 
carrying  a  drop  of  water  against  the  end  of  the  tube  (b),  when 
the  water  will  be  drawn  in. 

To  remove  any  excess  of  water  a  small  piece  of  filter-paper 
placed  at  b  may  be  used.  The  successful  adjustment  of  the 
meniscus  to  the  mark  a  requires  practice. 

The  pyknometer,  which  is  now  filled  with  a  definite  volume 
of  distilled  water  at  a  definite  temperature,  is  now  removed 
from  the  thermostat,  dried  with  a  cloth,  and  carefully  weighed. 
The  pyknometer  is  then  cleaned  and  dried  as  before,  and  filled 
with  the  liquid  to  be  tested.  The  volume  is  adjusted  in  the 
thermostat  exactly  as  before.  The  pyknometer  is  then  dried 
with  a  cloth  and  weighed. 

Calculation  —  The  apparent  weight  of  the  liquid  in  air  — 

We  =  [(pyknometer  +  liquid)  -  (pyknometer  +  air)]. 
The  weight  of  an  equal  volume  of  water  — 

Ww  =  [pyknometer  +  water)  -  (pyknometer  +  air)]. 
The  approximate  density  is  therefore  — 


This  is  usually  all  that  is  required. 


12       DENSITY  OF  GASES,  LIQUIDS,  AND  VAPOURS 

The  absolute  density  —  i.e.,  at  4°  C.  —  would  be  — 


where  Q  is  the  density  of  water  at  t. 

It  is  further  necessary  to  correct  for  the  buoyancy  of  the 
air  ;  therefore  for  the  final  expression  we  get  — 


-V 


W 


where  A  is  the  average  density  of  the   air  compared  with 
water,  and  may  be  taken  as  0*0012. 

Experiment  to  Determine  the  Density  of  Ethyl  Alcohol — Do 
this  by  the  method  described  above. 

Determination  of  the  Specific  Gravity  at  Higher  Temperatures, 
and  the  Determination  of  the  Molecular  Volume  of  Liquids  at 
Their  Soiling- Points — The  pyknometer  used  in 
this  case  is  as  indicated  in  Fig.  9.  It  con- 
sists of  a  thin  Jena  glass  bulb  about  3  c.c. 
capacity,  united  with  a  somewhat  longer, 
narrow  capillary  tube  with  a  turned-up  end. 

The  tube,  cleaned  and  dried,  is  first  weighed 
empty. 

The  pyknometer  may  be  conveniently  filled 
by  alternately  heating  and  cooling  the  bulb. 
Place  the  open  capillary  in  a  beaker  of  the 
liquid  to  be  tested,  and  immerse  the  bulb  in 
a  hot  bath  ;  after  a  minute  or  so  lift  the  bulb 
out  of  the  bath,  still  keeping  the  capillary  in 
the  liquid.  As  the  bulb  cools,  liquid  will 
be  drawn  over.  Repeat  this  several  times, 
gradually  raising  the  temperatures  of  the 
bath  until  only  a  very  small  bubble  of  air  remains  on 
cooling. 

The  almost  filled  pyknometer  is  suspended  in  a  wide- 
mouthed  boiling-flask  by  means  of  a  platinum  wire.  The 
flask  is  also  fitted  with  a  reflux  condenser  and  a  thermometer. 


FIG.  9 


DENSITY  OF  LIQUIDS 


13 


The  liquid  in  the  flask  is  the  same  as  in  the  pyknometer  (see 
Fig.  10). 


FIG.  10 

The  pyknometer  should  be  just  clear  of  the  surface  of  the 
liquid  when  it  is  boiling. 

When  the  liquid  in  the  flask  boils,  the  liquid  in  the  pyk- 
nometer expands,  carrying  with  it  the  last  traces  of  air,  until 
it  has  assumed  the  constant  temperature  equal  to  the  boiling- 
point  of  the  liquid. 

The  boiling  is  then  stopped,  and  the  pyknometer  allowed  to 
cool. 

It  is  then  taken  out,  dried,  and  weighed. 

Calculation — 

W9  =  [(pyk.  +  liq.)  -  (pyk.  +  air)] 
V0  =  volume  of  pyknometer  at  6°  C, 

where  0  =  boiling-point  of  the  liquid. 


14        DENSITY  OF  GASES,  LIQUIDS,  AND  VAPOURS 

Then  the  specific  gravity  will  be — 

A       W» 

A'=  \y 

Therefore  the  molecular  volume — 

v        m     m .  V0 

V™  =  A~  =  ~WT' 

where  m  is  the  molecular  weight  of  the  substance. 


CHAPTER  III 

DETERMINATION  OF  VISCOSITY  AND  SURFACE 
TENSION 

Viscosity — When  a  liquid  flows  through  a  tube,  the  velocity 
of  the  various  portions  of  the  liquid  differ  according  as  the 
liquid  is  in  contact  with  the  walls  of  the  tube  or  not.  That 
which  is  in  contact  with  the  walls  of  the  tube  moves  very 
slowly,  and  for  all  practical  purposes  may  be  considered  to  be 
at  rest.  The  next  layer  moves  with  a  slightly  greater 
velocity,  and  so  on,  the  liquid  at  the  axis  of  the  tube  having 
the  greatest  velocity.  Thus  we  get  a  sheaving  or  movement 
of  the  layers  one  over  the  other.  The  relative  velocity, 
therefore,  of  any  consecutive  layers  will  depend  upon  the 
internal  friction  or  viscosity  of  the  liquid.  For  the  same  tube, 
therefore,  the  velocity  of  the  respective  layers  will  increase 
more  rapidly  from  the  walls  of  the  tube  to  the  axis  the 
smaller  the  viscosity  of  the  liquid.  The  volume  of  liquid  which 
under  defined  conditions  flows  through  a  given  tube  will 
depend  on  the  viscosity  of  the  liquid. 

It  may  be  shown  that  for  the  flow  of  a  homogeneous  liquid 
through  a  capillary  tube  that — 


or 


Where  t  in  seconds  is  the  time  required  for  the  volume  V  of 
the  liquid  to  flow  through  a  tube  of  length  / ;  R  is  the  radius 
of  the  tube  ;  p  is  the  driving  power,  force,  or  excess  of  static 
pressure ;  77  is  the  co-efficient  of  viscosity  of  the  liquid.  The 
assumption  is  made  that  the  velocity  of  the  liquid  on  leaving 

15 


16 


VISCOSITY  AND  SURFACE  TENSION 


the  tube  is  zero.  As  this  is  not  the  case,  however,  it  is  neces- 
sary to  make  a  correction  for  the  kinetic  energy  of  the  liquid. 
For  all  practical  purposes  this  correction  may  be  omitted. 

Determination  of  the  Viscosity  of  Liquids:  Method  I— A 
simple  apparatus  for  the  determination  of  the  viscosity  of  a 
liquid  is  as  indicated  in  Fig.  11.  An  inverted  bell- jar,  fitted 
with  a  rubber  stopper,  through  which  passes  a  bent  tube, 
which  in  turn  is  connected  with  a  capillary  tube  of  known 


:o 


FIG.  11 

bore.  A  scale  is  gummed  on  to  the  side  of  the  bell -jar,  so 
that  the  height  of  the  liquid  before  and  after  the  experiment 
may  be  noted.  A  small  flask  with  a  graduation  mark  on  the 
neck  is  also  required.  Fill  to  a  convenient  level  the  bell-jar 
with  the  liquid  to  be  tested,  closing  the  exit  by  means  of  a 
pinch-cock  on  the  rubber  connection.  Note  the  temperature 
of  the  liquid.  Then  open  the  pinch-cock,  and  allow  the  liquid 
to  run  out  into  the  beaker  to  a  definite  mark  on  the  bell-jar 
scale.  At  that  instant  replace  the  beaker  by  the  graduated 
flask,  and  note  the  time  (in  seconds)  taken  to  fill  the  flask  up 


VISCOSITY 


17 


to  the  graduation  mark.  When  this  point  is  reached,  close 
the  pinch-cock,  and  again  note  the  level  of  the  liquid  in  the 
bell- jar. 

To  determine  the  mean  static  pressure,  p,  measure  the 
height  of  the  two  marks  on  the  bell-jar  scale,  and  subtract 
the  height  of  the  centre  of  the  bore  of  the  outlet  tube ;  then 
p  =  hgp,  where  h  is  the  mean  height,  g  gravity  acceleration,  and 
p  is  the  density  of  the  liquid. 

For  actual  calculation  see  next  experiment. 
Method  II — A  simpler  and  more  convenient  method  is  by 
using  Ostwald's  modification  of  Poiseuille's  apparatus  (Fig.  1 2). 
It  consists  essentially  of  a  definite  volume  bulb, 
a — 6,  to  which  is  attached  a  fine  capillary  tube, 
through  which  the  known  volume  of  liquid  is 
allowed  to  flow,  the  mean  driving-force  being 
equal  to  the  mean  static  pressure  due  to  the 
difference  in  the  level  in  the  two  limbs  of  the 
tube. 

Introduce  into  "c  "  a  definite  volume  of  the 
liquid  to  be  tested  by  means  of  an  accurate 
pipette.  Carefully  support  the  apparatus  in  a 
thermostat  with  transparent  sides  (a  large 
beaker  fitted  with  a  thermo-regulator  will  do). 
When  the  apparatus  has  attained  the  tem- 
perature of  the  bath,  adjust  the  level  of  the 
liquid  to  mark  "  a "  by  sucking  through 
"  e " ;  then  close  the  tap  e ;  then  open  tap  e>  and  carefully 
note  the  time  with  a  stop-watch  for  the  liquid  meniscus 
to  move  from  a  to  b.  This  should  be  repeated  four  or  five 
times,  and  the  mean  result  taken.  The  viscosity  varies 
considerably  with  temperature;  it  is  therefore  essential 
that  the  temperature  should  be  kept  constant  to  at  least 
0'1°  during  a  series  of  experiments.  A  suitable  tempera- 
ture to  work  is  25°  C.  A  suitable  exercise  is  the  determina- 
tion of  the  viscosity  of  benzene  relative  to  water.  The  influ- 
ence of  temperature  on  viscosity  is  determined  approximately 
by  repeating  the  experiment  at  intervals,  say,  of  5°  between 
25°  C.  and  50°  C.  and  plotting  the  results,  from  which  the 

temperature  co- efficient  ^r?  for  5°  can  be  calculated. 

The   absolute  value  in  C.Gr.S.  units   of  the  viscosity  co- 
efficient of  water  at  25°  C.  is  8-95  x  10-  . 
2 


FIG.  12 


18  VISCOSITY  AND  SURFACE  TENSION 

Calculation  —  The  force  which  drives  the  liquid  through  the 
capillary  will  be  equal  to  hgp,  where  h  is  the  mean  difference 
of  level  of  the  liquid  in  the  two  limbs  of  the  tube,  p  is  the 
density  of  the  liquid,  and  g  gravity  acceleration. 

Now,  if  the  experiment  is  repeated  with  a  second  liquid,  we 
get  the  "  driving  force  "  in  this  case  hgpv  from  which  we  see 
that  the  driving  force  is  proportional  to  the  densities  of  the 
liquids,  since  h  and  g  are  constants. 

The  "  co-efficients  of  viscosity  "- 


therefore  17  for  the  same  apparatus  is  proportional  to  the  driving 
force  p. 

Hence  we  get  — 

Tlz 

77l      gp^    pj 

This  gives  the  viscosity  of  the  second  relative  to  the  first, 
which  is  all  that  is  usually  required.  Water  is  usually  taken 
as  the  comparison  liquid.  The  co  efficient  in  absolute  units 
may  be  calculated  by  substituting  the  absolute  values  in  the 
equation  for  77. 

Surface  Tension  —  Capillarity  —  If  a  clean  glass  tube  of  fine 
bore  is  dipped  into  water,  the  water  rises  inside  the  tube. 
This  elevation  is  due  to  the  angle  of  contact  between  the  glass 
and  water  being  less  than  90°,  so  that  the  surface  tension 
tends  to  raise  the  water  near  the  glass. 

The  resolved  part  of  the  force  parallel  to  the  axis  of  the 
tube  is  27mr  cos  a  where  r  is  the  radius  of  the  tube,  o-  the 
surface  tension,  and  a  the  angle  of  contact. 

Now,  the  weight  of  liquid  up  the  tube  must  be  equal  to 
this  resolved  force,  and  this  latter  is  equal  to  irfihpg,  h  being 
the  height  in  the  tube,  and  p  the  density  of  the  liquid. 

/.  2  TITO-  cos  a  =  7rr2A/o<7. 

Now,  cos  a  is  usually  taken  as  1  in  cases  where  the  liquids 
wet  the  glass  : 


SURFACE  TENSION 


19 


The  value  of  o-  is  dependent  on  the  nature  of  the  liquid  and 
also  on  the  temperature. 

Now,  the  molecular  surface  of  different  liquids  will  contain 
the  same  number  of  molecules,  hence  the  product  of  the 
surface  tension  and  the  molecular  surface  of  different  liquids 
should  be  comparable  quantities. 

Now  the  molecular  surfaces  are  proportional  to  V$  where 
V  is  the  molecular  volume  ;  therefore  o-VS  represents  the 
molecular  surface  energy,  or  substituting  Mv  for  V  where  M  is 
the  molecular  weight  of  the  substance  and  v  is  the  specific 
volume,  we  get  o-Mv*. 

Now,  o-(Mv)§  is  a  linear  function  of  the  temperature  — 


where  T&  is  the  critical  temperature. 
Therefore  at  temperatures  Tx  and  T2  — 


^ 


The  value  of  K  is  the  same  for  different 
liquids  with  certain  exceptions,  and  has  a 
value  2-12. 

In  certain  cases,  particularly  when  the 
liquid  contains  hydroxyl  groups,  the  value 
obtained  for  K  is  less  than  2*12.  If,  how- 
ever, the  molecular  weight  is  multiplied 
by  a  factor  x  greater  than  one,  the  value 
2- 12  can  be  obtained. 

The  factor  x  is  termed  the  association 
factor,  and  represents  the  number  of  times 
the  mean  molecular  weight  of  the  liquid 
is  greater  than  the  normal  molecular  weight. 

Determination  of  Surface  Tension  of  Benzene  —  Fit  up 
apparatus  as  indicated  in  Fig.  13,  which  consists  of  a  boiling- 
tube  with  side  arm,  fitted  with  a  tight  rubber  stopper, 
through  which  passes  a  stout  capillary  tube.  A  graduated 
scale  is  fixed  on  to  the  capillary  tube. 

Put  some  benzene  into  the  boiling- tube,  and  place  the  whole 


FIG.  13 


20  VISCOSITY  AND  SURFACE  TENSION 

into  a  thermostat  at  25°  C.  When  the  apparatus  has  attained 
the  temperature  of  the  bath,  blow  slightly  through  the  side 
tube  so  as  bo  cause  the  benzene  to  rise  up  the  capillary,  and 
completely  wet  the  sides.  Then  by  means  of  a  telescope  read 
off  the  height  of  the  benzene  in  the  capillary  tube.  Three  or 
four  readings  should  be  made,  both  after  the  benzene  has  been 
made  to  rise  above  (by  blowing)  and  below  (by  sucking  at  the 
side  tube)  its  final  position. 
Then  from  equation— 

rpgh 


The  density  of  benzene  at  25°  C.  may  be  taken  as  0-8736. 

r  may  be  conveniently  found  by  measuring  carefully  a 
thread  of  mercury  in  the  capillary  and  then  weighing  it,  and 
calculating  r. 

w 


where  w  is  the  weight  of  the  mercury,  A  the  density  of  the 
mercury,  and  I  the  length  of  the  thread. 

From  these  data  the  surface  tension  can  now  be  calculated. 

To  Determine  the  Molecular  Surface  Energy  and  Association 
Factor  of  Ethyl  Alcohol  —  Repeat  the  above  experiment  with 
ethyl  alcohol  at  20°  and  40°,  and  calculate,  as  before  given. 
The  density  of  alcohol  at  20°  =  0-7894,  at  40°  =  0-7722. 

From  which  the  molecular  surface  energy  can  be  calculated 
thus  : 

<r=(M0)t 

(  v  specific  volume  =  T  -  r—  ). 
\  density/ 

Now,  for  an  associated  liquid  we  have  seen  that  — 

—A   LZ, 
2          l 

which  on  simplifying  gives  — 

2-12(T,-T1) 


Now,  all  terms  except  x  are  known,  therefore  the  degree  of 
association  can  be  easily  calculated. 


CHAPTER  IV 
DETERMINATION  OF  SOLUBILITY 

Solubility — When  a  solid  is  brought  into  contact  with  a  liquid 
in  which  it  is  soluble,  the  solid  continues  to  dissolve  until  a 
definite  concentration  is  reached.  The  solid  is  then  in  equil- 
ibrium with  the  solution  at  the  particular  temperature  of  the 
experiment.  When  such  conditions  exist,  the  solution  is  said 
to  be  saturated.  There  are  two  methods  usually  employed 
for  determining  the  solubility  of  solids  in  liquids. 

1.  Excess  of  the  finely  divided  solid  is  shaken  continuously 
with  a  definite  quantity  of  solvent  at  a  definite  temperature 
until  equilibrium  is  attained. 

2.  The  solvent  is  heated  with  excess  of  the  solute  to  a 
temperature  slightly  higher  than  that  at  which  the  solubility 
is  to  be  determined,  and  then  cooled  to  the  desired 
temperature  in  contact  with  the  solid.  $=-==5 

Solubility  curves  are  usually  continuous  so  long 
as  the  solid  phase  or  solid  substance  in  contact  with 
the  solution  remains  unchanged.  If,  however,  a 
change  in  the  solid  phase  does  occur,  the  solubility 
curve  will  show  a  break. 

This  is  the  case  with  sodium  sulphate.  The 
break  is  due  to  the  fact  that  we  are  dealing  with 
the  solubility  of  two  distinct  substances,  below  33°, 
Na2S0410H20,  and  above  33°,  anhydrous  (NaaS04). 

Experiment  to  Determine  the  Solubility   of  Sodium 
Sulphate — Take  a  stout  glass  tube,  as  indicated  in 
Fig.  14,  fitted  with  a  stirrer.     Introduce  a  quantity 
of  finely  powdered  Na2S0410H2O,  and  fill  the  tube 
about  two-thirds  with  distilled  water.     This  should         - 
then  be  fixed  in  a  thermostat  and  stirred  for  about     ^IG'  1' 
two  hours.     Then  allow  the  undissolved  solid   to 
settle,  remove  about  25  c.c.  with  a  pipette,  and  carefully 

21 


22  DETERMINATION  OF  SOLUBILITY 

evaporate  to  dryness  on  a  water-bath,  and  thus  determine 
the  amount  of  solid  dissolved  in  25  c.c.  of  water.  Then 
continue  the  stirring  for  another  hour,  taking  care  that  some 
of  the  solid  phase  is  always  present,  and  again  determine 
the  amount  of  solid  dissolved ;  repeat  until  constant  results  are 
obtained. 

Repeat  the  above  experiment  every  two  degrees  between 
25°  and  35°.  Express  the  solubility  in  grams  of  anhydrous 
salt  in  100  grams  of  water. 

Plot  your  results  graphically  and  determine  the  temperature 
of  the  break ;  this  is  the  transition  point  of — 

Na2S0410H20  «z=i>Na1S04+  10H20. 

Experiment  to  Determine  the  Solubility  Curve  of  Sodium  Chloride 
up  to  50°  C. — The  method  is  as  in  the  previous  experiment. 

Experiment  to  Determine  the  Solubility  Curve  of  Potassium, 
Chloride  up  to  50°  C. 

Observe  carefully  the  different  characteristics  of  the  three 
curves  obtained  from  the  above  experiments. 


CHAPTER  V 


DETERMINATION  OF  MOLECULAR  WEIGHTS 

IN  the  experiments  about  to  be  described  it  is  necessary  to 
use  a  thermometer  which  would  be  accurate  to  0*002  of  a 
degree.  At  the  same  time  it  is  not  usually  necessary  to  know 
the  exact  temperature,  but  only  changes  in  temperature. 

For  experiments  of  this  type  a  Beckmann  thermometer  is 
used.  It  usually  has  a  range  of  five  or  six  degrees,  and  is 
graduated  in  tenths  and  hundredths.  The  thermometer  is  so 
constructed  that  the  amount  of  mercury  in  the  bulb  can  be 
to  a  certain  extent  controlled.  This  is  rendered  possible  by 
having  at  the  upper  end  of  the  capillary  a  reservoir,  into 
which  any  excess  of  mercury  can  be  driven,  or  from  which 
further  mercury  can  be  drawn,  as  desired. 

To    set    a    Beckmann    Thermometer  —  First    invert    the 
thermometer,  and  collect  the  mercury  in  the  reservoir  at  the 
end  which  joins  on  to  the  capillary  (see 
Fig.  15).     Then  carefully  (so  as  not  to 
dislodge  the  mercury  in  the  reservoir) 
place  the  thermometer  in  a  beaker  of 
water ;    the  actual  temperature  of  the 
water  is  measured  by  an  ordinary  accu- 
rate  thermometer,    graduated  at  least 
in  tenths.     Now  regulate  the  tempera- 
ture of  the  bath  until  the  column  of 
mercury   in   the   capillary   joins    com- 
pletely the  mercury  in   the  reservoir.  FIG.  15 
Then  control   the   temperature   of  the 
bath  until  it  is  about  two  degrees  above  the  highest  tem- 
perature to  be  recorded   in  the  actual  experiment.     Allow 
the  thermometer  to  remain  at  this  temperature  for  several 
minutes,  and  then  strike  the  top  of  the  thermometer  sharply 

23 


24        DETERMINATION  OF  MOLECULAR  WEIGHTS 

with  the  palm  of  the  hand,  thus  causing  the  mercury 
in  the  reservoir  to  fall,  thereby  becoming  disconnected  from 
the  mercury  in  the  capillary.  Now  allow  the  temperature  of 
the  bath  to  fall  to  the  highest  temperature  to  be  reached  in 
the  actual  experiment.  If  the  setting  has  been  successful,  the 
mercury  in  the  capillary  should  stand  on  the  scale.  If  the 
mercury  stands  above  the  scale,  there  is  too  much  mercury  in 
the  bulb ;  if  too  low  on  the  scale,  the  mercury  in  the  bulb  is 
insufficient.  In  either  case  repeat  the  above  operation,  slightly 
raising  or  lowering  the  temperature  of  the  bath  at  which  the 
mercury  column  is  separated  from  the  reservoir,  until  the 
mercury  stands  at  a  convenient  height  on  the  scale  at  the 
highest  temperature  to  be  reached  in  the  experiment. 

Elevation  of  the  Boiling-Point — When  a  non-volatile  sub- 
stance is  dissolved  in  a  liquid,  the  vapour  pressure  of  the  liquid 
is  diminished ;  further,  this  diminution  is  proportional  to  the 
amount  of  solute  added.  Raoult,  in  1887,  after  much  experi- 
mental work,  came  to  the  following  conclusions  : 

1.  Equimolecular    quantities   of  different   substances,   dis- 
solved in  equal  volumes  of  the  same  solvent,  lower  the  vapour 
pressure  to  the  same  extent. 

2.  The  relative  lowering  of  the  vapour  pressure  is  equal  to 
the  ratio  of  the  number  of  molecules  of  solute,  and  the  total 
number  of  molecules  in  solution. 

A  liquid  boils  when  its  vapour  pressure  is  equal  to  that  of 
the  atmosphere.  In  the  presence  of  a  solute  the  difference 
between  the  vapour  pressure  of  the  solution  and  the  atmo- 
sphere is  greater  than  in  the  case  of  the  pure  solvent,  hence  in  , 
the  case  of  a  solution  a  slightly  higher  temperature  is  required 
than  for  the  pure  solvent  to  produce  the  slightly  extra 
pressure. 

It  follows  also  that  the  elevation  in  temperature  will  be 
proportional  to  the  lowering  of  the  vapour  pressure.  Hence 
Raoulfs  law  may  be  re-interpreted  thus  :  Equimolecular  quantities 
of  different  solutes,  in  equal  volumes  of  the  same  solvent,  produce  the 
same  elevation  of  the  boiling-point.  It  is  therefore  possible  to 
determine  the  molecular  weight  of  any  soluble  substance  by 
comparing  its  effect  on  the  boiling-point  of  a  solvent  with 
that  of  a  substance  of  known  molecular  weight. 

If  x  grams  of  the  substance  of  molecular  weight  m  (where 
m  is  to  be  determined)  be  dissolved  in  W  grams  of  solvent, 
raise  the  boiling-point  by  8  degrees,  whilst  m  grams  in 


ELEVATION  OF  THE  BOILING-POINT  25 

100  grams  of  solvent  give  a  rise  of  K  degrees,  then  we 
have  — 

x     «  •  .   m      K- 
W  5  '  '  TOO  '  K' 

KalOO 

Van't  Hoff  has  shown  that  K  (which  is  termed  the  molecular 
elevation,  constant)  can  be  calculated  from  the  latent  heat  of 
vaporization  of  the  solvent,  and  its  boiling-point  on  the  abso- 
lute scale  : 

_     0-02T2 

~H~' 

where  T  is  the  boiling-point,  and  H  the  latent  heat  of  vaporiza- 
tion ;  hence  we  get  — 

0-02T* 


Method  I:  Beckmanrfs  Method  —  The  apparatus,  as  is 
shown  in  Fig.  16,  consists  of  a  boiling-tube,  A,  to  the  side  arm 
of  which  is  attached  a  coiled  condenser,  Kv  and  through  the 
upper  stopper  of  which  is  introduced  a  Beckmann  ther- 
mometer. 

A  stout  bit  of  platinum  wire  is  fused  through  the  bottom  of 
A,  and  a  few  glass  beads  are  introduced  to  ensure  uniform 
ebullition.  This  boiling-tube  is  surrounded  by  a  jacket,  B, 
which  is  made  of  glass  (porcelain  or  copper  for  high  tempera- 
tures), which  is  also  fitted  with  a  coiled  condenser,  K2. 

The  vapour  jacket  is  supported  by  a  small  asbestos  box,  C, 
which  is  so  constructed  that  the  flames  do  not  come  directly 
under  the  boiling-  tube  A  (see  section).  Two  chimneys,  St  carry 
the  hot  gases  from  the  flames  away  from  the  apparatus.  If 
the  solvent  boils  below  60°  C.,  the  coiled  condensers  should  be 
replaced  by  small  water  condensers,  which  may  be  joined  up 
in  series.  For  hygroscopic  solvents,  calcium  chloride  tubes 
should  be  attached  to  the  condensers. 

Experiment  to  Determine  the  Molecular  W  'eight  of  Camphor  in 
Ethyl  Alcohol  —  Weigh  out  carefully  into  the  boiling-tube 
15  grams  of  ethyl  alcohol,  introduce  also  a  few  clean  dry  glass 


20        DETERMINATION  OF  MOLECULAR  WEIGHTS 

beads.  See  that  bulb  of  the  thermometer  is  just  below  the 
surface  of  the  liquid.  Introduce  into  the  outer  jacket  a  con- 
venient quantity  of  alcohol  (containing  a  little  water,  or  a  few 
drops  of  higher  boiling  liquid).  Put  in  also  one  or  two  pieces  of 


FIG.  16 


porous  tile.  Then  bring  the  liquid  in  the  outer  jacket  to  a  steady 
boil,  this  will  eventually  cause  the  pure  alcohol  in  A  to  boil. 
When  the  Beckmann  reading  has  remained  steady  for  at  least 
five  minutes,  note  the  reading,  and  allow  the  apparatus  to  cool 
down  ;  and  then  introduce  into  A  a  small  tabloid  of  camphor 


ELEVATION  OF  THE  BOILING-POINT 


27 


(about  0-5  gram)  accurately  weighed.  Now  bring  the  liquid 
to  boiling  again,  and  when  the  reading  on  the  thermometer 
is  constant,  note  the  temperature.  It  is  essential  that  the  rate 
of  boiling  should  be  as  near  equal  as  possible  in  both  cases ; 
this  may  be  judged  by  noting  the  rate  at  which  the  drops  fall 
back  from  the  condenser  attached  to  A.  The  thermometer 
should  also  be  tapped  before  each  reading,  as  the  mercury 
column  is  very  liable  to  stick.  The  barometric  height  should 
also  be  taken  at  each  reading,  and  corrections  applied,  if  neces- 
sary. Repeat  the  experiment,  using  0*75  gram  of  camphor. 
Latent  heat  of  vaporization  of  ethyl  alcohol  is  216*5  cals., 


FIG.  17 

B.P.  78-4° ;  benzene  may  be  used  instead  of  ethyl  alcohol  as  a 
solvent. 

Experiment  to  Determine  the  Molecular  Weight  of  Ethyl 
Benzoate  in  Benzene — In  this  case  the  liquid  is  introduced  by 
means  of  a  special  pipette  (see  Fig.  17).  The  pipette  contain- 
ing the  ethyl  benzoate  is  first  accurately  weighed,  and  then  a 
quantity  introduced  into  the  apparatus,  and  then  weighed 
again.  The  loss  represents  the  amount  of  solute  used. 
Latent  heat  of  vaporization  of  benzene,  93  cals.,  B.P.  80°. 

Method  II:  Electrical  Heating  —  A  modified  and  much 
more  convenient  form  of  apparatus  is  indicated  in  Fig.  18. 
It  consists  of  a  boiling-tube  fitted  into  a  Dewar  flask.  Two 
narrow  tubes,  t,  t,  pass  through  cork,  W,  through  the  lower  end 


28        DETERMINATION  OF  MOLECULAR  WEIGHTS 

of  each  is  sealed  a  piece  of  fairly  stout  platinum  wire,  and 
from  these  two  wires  is  suspended  the  heating-coil. 

The  coil  consists  essentially  of  a  glass  spiral,  which  is  broken 
in  the  middle  at  M.  Through  this  spiral  is  threaded  fine 
platinum  wire  (about  0*25  mm.  diameter).  The  two  ends 
of  this  wire  are  then  fastened  to  the  two  stout  wires,  so  that 
the  coil  hangs  vertically,  and  also  symmetrically  with  respect  to 


FIG.  18 

the  thermometer.  A  quantity  of  mercury  is  introduced  into 
the  tubes  t,  t,  so  that  by  means  of  copper  wires  inserted  into 
the  open  end,  so  as  to  touch  the  mercury,  the  heating-coil  may 
be  connected  with  the  source  of  electricity.  A  current  from 
four  or  five  accumulators,  giving  a  current  of  6  to  8  amperes, 
will  usually  be  sufficient. 

By  having  a  glass  spiral  surrounding  the  wire  the  bulk  of 
the  liquid  is  eventually  heated  by  its  own  vapour  as  it 
vaporizes  within  the  spiral.  In  order  to  prevent  superheating 


ELEVATION  OF  THE  BOILING-POINT 


29 


it  is  essential  to  see  the  bubbles  are  issuing  from  the  opening 
in  the  middle  M  and  at  the  bottom.  If  bubbles  come  only 
from  the  middle  and  top,  superheating  is  very  probably  taking 
place ;  this  can  be  remedied  by  tapping  the  apparatus.  The 
experiment  described  under  Method  I  may  be  carried  out 
with  this  apparatus  in  a  similar  manner. 

Landsberger's  Method — In  this  method  the  solution  is  brought 
to  boiling-point  by  passing  into  it  the  vapour  of  the  solvent.    In 


FIG.  19 

this  case  there  can  be  no  fear  of  superheating,  as  the  tempera- 
ture of  the  vapour  is  lower  than  that  of  the  boiling  solution. 
The  apparatus  consists  essentially  of  a  graduated  tube,  T,  with 
a  small  outlet  at  0.  This  tube  is  surrounded  by  a  wider 
tube,  L,  which  has  a  tube  at  the  bottom  to  lead  the  vapours  to 
a  condenser.  The  thermometer  E  should  be  graduated  in 
tenths.  The  pure  solvent  is  boiled  in  flask  H,  from  which  the 
vapour  is  led  into  T  by  tube  K.  The  tube  X  is  merely  a 
safety  valve. 

Experiment — Fit  up  the  apparatus  as  shown  in  Fig.   19. 
Introduce  into  H  a  quantity  of  pure  alcohol  (also  a  few  pieces 


30        DETERMINATION  OF  MOLECULAR  WEIGHTS 

of  porous  tile).  Place  about  10  c.c.  of  alcohol  in  T.  Boil 
the  alcohol  in  H,  and  pass  the  vapour  into  the  alcohol  in  T. 
Regulate  the  heating  of  the  liquid  in  H  so  that  when  the 
alcohol  boils  in  T  the  condensed  vapour  issues  from  the  con- 
denser at  about  one  drop  in  two  seconds.  When  the  tempera- 
ture is  constant,  read  off  the  boiling-point  of  the  solvent. 
Remove  some  of  the  solvent  which  has  accumulated  in  T 
until  about  6  or  7  c.c.  remain  Fill  up,  if  necessary,  flask  H. 
Now  introduce  into  T  a  small  tabloid  of  camphor,  and  repeat 
the  above  process,  taking  care  that  the  rate  at  which  the 
solvent  issues  from  the  condenser  is  similar  to  that  in  the  pre- 
vious case.  Note  the  temperature  when  practically  constant. 
Then  turn  out  the  flame  under  the  boiler,  and  rapidly  discon- 
nect from  the  rest  of  the  apparatus.  Then  read  off  accurately 
the  volume  of  liquid  in  T  to  a  tenth  of  a  centimetre.  Reconnect 
with  the  boiler,  and  repeat  the  experiment  three  times.  On 
each  occasion  the  volume  of  solution  in  T  will  change,  but  for 
each  volume  there  will  be  a  corresponding  temperature  ;  for 
in  each  case  the  concentration  of  the  solute  will  be  different, 
hence  the  change  in  the  boiling-point. 

Note  —  It  is  advisable  to  renew  the  porous  tile  in  H  after 
each  disconnection. 

Calculation  —  In  this  the  equation  will  be  — 

KzlOO 


where  V  is  the  volume  read  off,  and  S  the  density  of  alcohol 
at  the  temperature  at  which  the  reading  is  made  (boiling- 

point).    The  ratio  -g  is  sometimes  known  as  the  constant  of 

Landsberger's  method. 

17- 

Hence,  if  we  put  C  =  -Q,  we  get  — 

CslOO 
~V8~* 
C  for  alcohol  =15-6. 

Compare  the  results  obtained  by  this  method  with  those 
obtained  by  Beckmann's  method. 


DEPRESSION  OF  THE  FREEZING-POINT 


31 


Experiment  to  Determine  the  Molecular  Weight  of  Benzoic  Acid 
in  Ether  by  the  Method  described  above  : 

Depression  of  the  Freezing-Point — Where  possible,  this 
method  is  used  in  preference  to  the  boiling  method,  because 
much  more  accurate  determinations  can  be  made. 

The  apparatus  is  due  to  Beckmann,  and  is  as  shown  in 
Fig.  20.  The  inner  tube  A,  which  is  provided  with  a  ther- 
mometer and  stirrer,  and  also  a  side 
tube,  contains  the  solvent,  the  freezing- 
point  of  which  is  to  be  determined. 

A  is  fastened  to  the  wider  tube  B 
by  means  of  a  cork,  which  is  in  turn 
supported  by  a  metallic  cover  in  the 
bath  (7,  in  which  the  freezing  mixture 
is  placed.  The  vessel  C  is  provided 
with  a  stirrer  and  also  vessel  A  ;  in 
the  latter  case  it  should  be  of  platinum, 
but,  without  any  serious  error  it  may 
be  of  glass.  The  depression  in  freezing- 
point  is  determined  by  means  of  a 
Beckmann  thermometer,  which  is  fitted 
by  means  of  a  cork  in  A.  Between  B 
and  A  is  an  air  mantle,  which  controls 
the  fall  in  temperature  by  causing  the 
solvent  to  cool  gradually.  In  carry- 
ing out  an  experiment  the  tempera- 
ture of  the  freezing  mixture  should 
not  be  more  than  3°  or  4°  below  the 
freezing-point  of  the  solvent,  and, 
further,  the  temperature  of  the  bath 
should  be  kept  as  constant  as  possible. 

Method  —  In  an  experiment  about 
20  grams  of  solvent  are  introduced 
into  A  ;  stir  the  solvent  uniformly 
(not  too  vigorously),  and  from  time 
to  time  stir  the  freezing-bath.  Owing 
to  the  supercooling  this  temperature  falls  below  the  freezing- 
point  of  the  solvent,  but  as  soon  as  any  solid  begins  to 
separate  out  the  temperature  rises  again,  owing  to  the 
evolution  of  the  latent  heat  of  fusion  of  the  solvent.  The 
amount  of  supercooling  can  be  reduced  by  the  introduction  of 
a  crystal  of  solvent  as  soon  as  the  temperature  falls  below  the 


FIG.  20 


32        DETERMINATION  OF  MOLECULAR  WEIGHTS 

freezing-point.  The  highest  temperature  observed  after  the 
formation  of  solid  is  taken  as  the  freezing-point,  because  the 
temperature  cannot  rise  naturally  above  the  melting-point  of 
the  solid  while  solid  is  still  present.  (A  slight  error  is  intro- 
duced due  to  the  friction  of  the  stirrer  in  A,  and  also  conduc- 
tion from  outside  by  stirrer,  thermometer,  etc.,  but  this  need 
not  be  considered  here.)  A  is  now  removed  and  accurately 
weighed,  a  quantity  of  the  solute  added,  and  the  determination 
of  the  freezing-point  repeated.  If  the  temperature  of  the 
freezing-bath  has  also  been  carefully  adjusted,  the  solvent  will 
separate  out  slowly,  and  the  highest  temperature  reached  soon 
after  the  formation  of  a  little  solid  is  taken  as  the  freezing- 
point.  If,  however,  the  temperature  of  the  bath  is  too  low,  or 
there  is  considerable  supercooling,  the  separation  of  solid 
solvent  will  be  too  great,  and  the  temperature  of  this  equil- 
ibrium will  be  that  of  a  much  more  concentrated  solution  than 
that  originally  prepared,  and  the  more  concentrated  the  solu- 
tion, the  greater  is  the  depression  produced. 

Calculation  —  The  calculation  is  made  by  a  similar  method  to 
that  used  in  the  case  of  boiling-point  determinations. 

KzlOO 

-WA—m' 

where  A  is  the  depression. 

0-02T2 
K,  as  before, 


Experiment  to  Determine  the  Molecular  freight  of  Acetone  in 
Acetic  Acid  —  Introduce  into  A  25  grams  of  pure  glacial  acetic 
acid.  Use  as  a  bath  water  at  about  12°  to  13°.  Determine 
the  freezing-point  as  described  above.  Now  introduce  by 
means  of  a  pipette  (see  Fig.  17)  about  0-5  gram  of  acetone 
(determine  weight  by  difference),  and  redetermine  the  freezing- 
point. 

Experiment  to  Determine  the  Molecular  Weight  of  Napthalene 
in  Benzene  —  Use  a  bath  of  ice  and  water  giving  a  temperature 
of  about  2°  C.  Where  the  temperature  of  the  solvent  is  a 
fair  way  off  its  freezing-point,  preliminary  cooling  may  be 
done  by  immersing  tube  A  directly  in  the  freezing-bath  until 
the  solvent  is  within  1°  or  2°  of  its  freezing-point.  Use 
0*25  gram  of  napthalene  in  25  grams  of  solvent. 


ABNORMAL  MOLECULAR  WEIGHTS  33 

Abnormal  Molecular  Weights— It  frequently  happens  the 
molecular  weights  obtained  by  the  above  method  do  not  agree 
with  those  obtained  by  other  methods.  They  are  in  some 
cases  greater  and  in  other  cases  less.  Now,  the  depression  of 
the  freezing-point  is  proportionate  to  the  number  of  molecules 
dissolved  in  a  given  volume  of  solvent.  Hence  the  only 
conclusion  is  that  the  number  of  molecules  in  solution  is 
greater  or  less  than  it  should  be — i.en  dissociation  or  association 
has  taken  place.  Consider  the  case  of  association  :  Let  x  be 
the  degree  of  association,  then  1  -  x  represents  the  unassociated 
molecules.  If  n  represents  the  complexity  of  the  associated 

/£ 

molecules,  then  —  will  represent  the  number   of   associated 
molecules.     Hence  in   a  molecular   solution  the  number  of 

/j* 

molecules  will  have  been  reduced  in  the  ratio  1  :  ].-x  +  -- 

71 

Therefore  the  decrease  of  the  observed  depression  from  the 
theoretical  depression  will  be  in  the  ratio  of — 


where  A0  is  the  observed  depression,  and  A,  the  calculated 
depression.     Hence — 


x  = 


or  since 


we  get 

M0-M( 


34        DETERMINATION  OF  MOLECULAR  WEIGHTS 

If  dissociation  takes  place,  the  equation  becomes  — 


or 

Mt-U 


Mo(n  -  1)' 

By  applying  the  above,  the  degree  of  association  or  dissocia- 
tion of  a  solute  may  be  determined. 
Suppose  in  equation  — 

KzlOO  /1X 

m=    WA~       .        .         .         •     (1) 

we  assume  m  from  other  sources  and  calculate  K,  and  compare 
it  with  the  value  obtained  from  Van't  HofFs  equation  — 

K 


H 

If  association  has  taken  place,  K  will  be  less  ;  if  dissociation, 
greater  in  equation  (1)  than  in  equation  (2). 

Example  K  for  cane  sugar  in  water  is  18  '6,  for  sodium 
chloride  in  water  36*0,  for  methyl  iodide  in  benzene  50  -4,  for 
benzoic  acid  in  benzene  25*4.  The  normal  values  are  18-6  and 
51*2  in  water  and  benzene  respectively. 

Note  —  One  value  of  K  is  approximately  double  the  other 
for  each  solvent. 

Experiment  to  Determine  the  Apparent  Molecular  Weight  of 
Potassium  Chloride  in  Water,  and  from  the  Result  Calculate  the 
Degree  of  lonization  —  Carry  the  determination  as  in  previous 
experiment.  Introduce  a  crystal  of  ice  to  prevent  excessive 
supercooling. 


CHAPTER  VI 
DETERMINATION  OF  TRANSITION  POINTS 

MANY  substances  are  capable  of  existing  in  two  or  more 
crystallized  forms,  but  the  various  forms  are  not  equally 
stable  under  the  same  conditions. 

Sulphur  is  one  of  the  best  known  examples.  Rhombic 
sulphur  is  stable  at  ordinary  temperatures,  and  on  heating 
melts  at  115°  C.  On  being  kept  for  a  time  at  about  100°  C. 
it  changes  completely  into  the  monoclinic  variety,  which  has  a 
melting-point  of  120°.  Monoclinic  sulphur  can  be  kept  for 
an  indefinite  period  at  temperatures,  say,  100°  to  110°  C.  with- 
out undergoing  any  further  change.  Rhombic  sulphur 
however,  changes  to  monoclinic  at  these  temperatures. 
Monoclinic  sulphur  is  therefore  the  stable  form  under  these 
conditions.  Thus  there  is  a  temperature  above  which  mono- 
clinic  sulphur  is  the  stable  form,  and  below  which  rhombic 
sulphur  is  the  stable  form,  and  at  which  the  two  forms  are  in 
equilibrium  with  their  vapour — i.e.,  a  temperature  at  which 
neither  form  changes  into  the  other  on  keeping.  This  tem- 
perature is  termed  the  transition  temperature,  or  transition  point, 
and  is  in  the  case  of  sulphur  95'6°  C. 

When  a  salt  combines  with  water  to  form  more  than  one 
hydrate,  it  is  found  that  only  one  hydrate  is  stable  under  any 
given  conditions  of  temperature,  etc.,  or  conditions  may  arise 
when  the  anhydrous  salt  is  the  stable  variety.  Thus,  we 
find  transition  points  in  the  case  of  salt  hydrates,  that  is  to 
say,  on  passing  a  certain  temperature  the  composition  of  the 
salt  hydrate  changes  to  another  definite  composition,  while  at 
this  temperature  the  two  definite  hydrates  (or  anhydrous 
salt)  can  co-exist. 

Thus  on  heating  sodium  sulphate  decahydrate  to  a  tempera- 
ture above  33°  C.  it  is  found  that  decomposition  occurs  into 

35 


36 


DETERMINATION  OF  TRANSITION  POINTS 


anhydrous  sodium  sulphate  and  a  saturated  solution  of  the 
anhydrous  salt. 

If,  on  the  other  hand,  a  saturated  solution  of  sodium  sulphate, 
at  say  40°  C.,  in  presence  of  an  anhydrous  salt,  be  allowed  to 
cool,  when  the  temperature  has  fallen  below  33°  C.  the 
anhydrous  salt  takes  up  water  and  forms  decahydrate  crystals. 
33°  is  therefore  approximately  the  transition-point  for  the 
change. 

Na2S0410H20^==>Na2S04+  10H20. 

Determination  of  the  Transition-Point — (1)  Thermometric 
Method — When  one  system  changes  into  another,  the  change 
is  almost  invariably  accompanied  by  some  heat  effect,  either 
absorption  or  evolution  of  heat.  Thus,  on  heating,  say 
Na2S0410H2O,  the  temperature  rises  normally  until  the 
decahydrate  begins  to  change  into  the  anhydrous  form;  at 
this  point  the  temperature  remains  practically  stationary 
until  the  transformation  is  complete,  since 
heat  is  absorbed  by  this  change.  Hence, 
by  noting  the  temperature  at  which  this 
/?  retardation  occurs,  the  transition-point  may 
be  determined.  When  the  reverse  change 
is  allowed  to  take  place,  there  is  an  evolu- 
tion of  heat. 

In  actual  experiment  it  is  usual  to  plot 
both  the  heating  and  cooling  curves. 

Experiment  to  Determine  the  Transition-Point 
of  Sodium  Sulphate — Take  about  40  grams 
of  pure  sodium  sulphate  decahydrate  in  a 
thin    glass    boiling  -  tube.      Hang    a   ther- 
mometer,  which   should    be   graduated    in 
tenths  of  a  degree,  so  that  the  bulb  is  com- 
)letely    surrounded    by    the     decahydrate. 
support    the   tube    in    a   large   beaker   of 
FIG.  21          water,  which  can  be  heated  very  gradually 
with  a   small   flame.     The   temperature  of 
the   bath   should  be  kept  uniform  by  means    of  a  stirrer 
(see  Fig.  21).     Eaise  the  temperature  of  the  bath  to  about 
31°  C.,  and  then  keep  the  temperature  constant  for  a  short 
time.     Now  very  slowly  raise  the  temperature  until  the  salt 
becomes  partially  liquid.     At  this  stage  the  salt  should  also  be 
kept  constantly  stirred.     The  rate  of  rise  in  temperature  at 


DILATROMETR1C  METHOD  37 

this  stage  should  not  be  more  than  about  1°  in  10  minutes. 
When  the  salt  has  begun  to  liquify,  the  temperature  should 
be  read  every  minute.  A  point  is  reached  at  which  the 
temperature  is  practically  stationary  for  an  interval.  This  is 
due  to  the  absorption  of  heat  during  the  transition  from  the 
decahydrate  to  the  anhydrous  salt  and  solution. 

After  a  time  the  temperature  begins  to  rise  gradually 
again.  When  the  temperature  has  reached  about  36°  C., 
allow  to  cool,  stirring  constantly,  the  bath  and  the  salt. 
Again  take  readings  every  minute ;  a  period  of  approximate 
constancy  will  be  noted,  in  this  case  due  to  the  evolution  of 
heat,  owing  to  the  reformation  of  the  decahydrate.  Now 
plot  these  temperature  readings  against  time,  and  draw  the 
two  curves,  one  for  rising  temperature  and  the  other  for 
falling  temperature.  Theoretically  one  would  expect  these 
two  curves  to  be  identical.  They  are  both  of  the  same  type, 
but  the  vertical  portions  do  not  coincide. 

This  lack  of  coincidence  of  the  two  curves  is  due  to  what 
is  termed  suspended  transformation.  At  the  higher  tempera- 
ture we  are  dealing  with  a  solution  of  the  anhydrous  salt,  and 
after  passing  below  the  transition-point,  it  is  possible  for  the 
solution  of  the  anhydrous  salt  to  exist,  if  the  stable  phase,  in 
this  case  the  decahydrate,  is  entirely  absent.  Such  a  solution 
is,  however,  unstable.  The  amount  of  lag  can  be  considerably 
reduced  by  vigorous  stirring  in  the  neighbourhood  of  the 
transition-point. 

The  amount  of  lag  can  also  be  reduced  by  allowing  the 
temperature  to  change  very  slowly  in  the  neighbourhood  of 
the  transition -point. 

The  general  type  of  such  curves  is  as  indicated  at  Fig.  22. 

(2)  Dilatrometric  Method — This  method  depends  upon  the 
fact  that  change  from  one  system  to  another  on  passing 
through  the  transition-point  is  accompanied  by  an  appreciable 
change  in  volume,  and  it  is  only  necessary  to  determine  the 
temperature  at  which  this  change  of  volume  occurs  in  order 
to  ascertain  the  transition-point.  This  variation  in  volume  is 
studied  by  means  of  a  dilatometer,  which  consists  of  a  long 
capillary  tube  about  0*5  mm.  internal  diameter,  to  which  is 
attached  a  long  bulb  (Fig.  23). 

Experiment  to  Determine  the  Temperature  of  Foi'mation  of  Astra- 
canite  from  the  Simple  Salts — Take  equimolecular  weights  of 
sodium  sulphate  decahydrate,  and  magnesium  sulphate  hepta- 


DETERMINATION  OF  TRANSITION  POINTS 


hydrate ;  powder  each  up,  and  mix  them  by  stirring  with  a 
glass  rod.     Protect  the  capillary  tube  by  a  small  glass  bead, 


Temperature 
FIG.  22 


V 


FIG.  23 


and  then  introduce  some  of  the  mixture  into  the  bulb,  filling 
it  about  three-quarters  full ;  then  seal  off  the  open  end  of  the 
bulb;  invert  and  shake  the  solid  mixture 
down  to  the  bottom  of  the  bulb.  It  now 
remains  to  fill  the  rest  of  the  bulb  and 
part  of  the  capillary  with  some  suitable 
liquid.  To  do  this  fix  an  adapter  to  the 
capillary  (as  shown  in  Fig.  24),  and  intro- 
duce a  quantity  of  xylene.  Attach  the 
adapter  to  a  water-pump  and  exhaust  the 
dilatometer,  then,  on  suddenly  admitting  the 
air,  the  xylene  will  be  driven  down  into 
the  bulb.  This  operation  is  repeated  until 
all  the  air  has  been  removed.  It  is  neces- 
sary to  tap  the  tube  to  remove  any  air  which 
is  entrained  in  the  solid  mixture.  Fix  some 
suitable  scale  to  the  capillary,  and  adjust 
the  meniscus  by  pushing  a  piece  of  thin 
platinum  wire  down  the  capillary,  and  thus 
driving  out  some  of  the  xylene.  Immerse  the  bulb  of  the 


FIG.  24 


VAPOUR  PRESSURE  METHOD 


dilatometer  in  a  beaker  of  water  at  16°  C.,  and  note  the 
height  of  the  meniscus.  Raise  the  temperature  1°  at  a  time, 
and  take  reading  of  the  height  of  the  meniscus,  each  degree 
each  time  waiting  until  the  meniscus  has  come  to  rest ;  con- 
tinue up  to  25°  0.  Now  allow  the  bath  to  cool,  and  again 
take  readings  every  degree,  and  so  obtain  a  cooling  curve. 
Plot  the  results  obtained — i.e.,  plot  the  heights  of  the  meniscus 
as  ordinates  against  temperature  readings.  An  abrupt 
increase  in  volume  will  be  noted 
about  21°  to  22°  on  the  heating 
curve,  and  an  abrupt  contraction 
on  the  cooling  curve  at  about 
the  same  temperature.  The  two 
curves,  however,  do  not  coincide, 
the  expansion  taking  place  at  a 
slightly  higher  temperature,  and 
the  contraction  at  a  slightly  lower 
temperature,  than  the  true  transi- 
tion-point. The  curves  are  very 
similar  to  those  obtained  in  the 
previous  experiment. 

(3)  Vapour  Pressure  Method 
—When  one  system  can  be  trans- 
formed into  another,  the  vapour 
pressures  of  the  two  systems  are 
identical  at  the  transition-point. 
This  method  has,  so  far,  only 
been  applied  to  systems  contain- 
ing water  or  other  volatile  com- 
ponent. For  the  purpose  of 
making  these  measurements  a 
differential  manometer  is  used. 
The  most  convenient  form  is 
known  as  Bremer-Frowein  tensi-  FIG.  25 

meter,    which    is    as    shown    in 

Fig.  25.  It  consists  of  a  U  tube,  the  limbs  of  which  are  bent 
close  together,  and  backed  by  a  millimetre  scale.  The  bend 
is  filled  with  oil,  or  bromnaphthalene,  or  some  other  suitable 
liquid. 

The  substances  the  vapour  pressures  of  which  are  to  be  com- 
pared are  placed  in  the  bulb  a,  b,  and  the  necks  then  sealed  off. 
The  apparatus  is  then  inclined  so  that  the  liquid  in  the  bend 


-=-    „ 


40  DETERMINATION  OF  TRANSITION  POINTS 

collects  in  the  bulbs  c,  d.  The  open  end  e  is  then  connected 
to  a  mercury  pump,  and  the  apparatus  completely  evacuated. 
The  tube  e  is  then  sealed  off.  The  apparatus  is  then  placed 
perpendicularly  in  a  thermostat,  and  the  differences  in  level 
read. 

Experiment  to  Determine  the  Transition  of  Sodium  Sulphate — 
In  this  case  fill  the  bend  of  the  tube  with  bromnaphthalene, 
and  into  the  bulbs  a,  b  respectively  introduce  pure  dry  powdered 
crystals  of  the  decahydrate,  and  crystals  moistened  with  a 
little  water  so  as  to  make  a  saturated  solution.  Exhaust  the 
apparatus  and  seal  off  as  previously  indicated,  and  place  the 
tensimeter  perpendicularly  in  the  thermostat  at  25°  C.,  allow 
the  difference  in  pressure  to  become  constant,  and  then  read 
it  off.  Then  slowly,  as  before,  raise  the  temperature,  noting 
each  degree  the  difference  in  pressure.  At  the  transition  - 
point  the  vapour  pressure  of  the  crystals  of  decahydrate  must 
become  equal  to  that  of  a  solution  saturated  with  the  deca- 
hydrate and  anhydrous  salt. 

(4)  Solubility  Method— The  transition-point  of  Glauber  salts 
may  be  determined  by  plotting  the  solubility  for  the  an- 
hydrous salt  and  the  decahydrate  respectively.  The  point  of 
intersection  of  the  two  curves  gives  the  transition-point. 
The  experimental  details  of  this  method  are  indicated  in  the 
chapter  on  Solubility. 


CHAPTER  VII 
OSMOTIC  PRESSURE 

WHEN  a  dilute  solution  of  a  substance  in  water  is  placed 
in  a  vessel  closed  with  an  animal  membrane,  such  as  a 
bladder,  and  the  whole  immersed  in  water  to  a  depth 
that  the  level  of  the  water  outside  is  the  same  as  the  level 
of  the  solution  inside,  it  is  observed  that  the  volume  of 
the  liquid  in  the  inner  vessel  increases,  and  this  is  made 
manifest  by  the  rise  of  the  liquid  in  the  vessel.  It  is  obvious 
from  this  experiment  that  water  must  have  passed  from  the 
outer  vessel  through  the  membrane  to  the  inner  vessel  But 
if  the  outside  liquid  is  examined,  a  quantity  of  solute  will  be 
found  to  be  present.  Hence  some  of  the  solution  must  have 
found  its  way  through  the  membrane.  After  the  solution  has 
risen  to  a  certain  height  in  the  vessel,  the  liquid  begins  to  fall 
gradually,  due  to  the  fact  that  the  solutions  continues  to  pene- 
trate the  membrane. 

Many  attempts  were  made  to  find  some  general  relation- 
ship between  the  height  the  liquid  rose  in  the  vessel  and  the 
concentration  of  the  solution.  But  at  first  this  was  found 
impossible,  since  the  amount  of  solution  which  escaped  varied 
with  different  membranes.  Later,  however,  it  was  discovered 
(Traube  1867,  Pfeffer  1877)  that  artificial  membranes  could 
be  prepared  which,  while  allowing  the  passage  of  water 
through  them  just  as  in  the  case  of  animal  membranes,  unlike 
these  materials,  they  offered  a  perfect  barrier  to  the  passage  of 
many  substances  in  solution  in  the  water.  If  a  solution  of 
copper  sulphate  is  brought  very  carefully  in  contact  with  a 
solution  of  potassium  ferrocyanide,  a  delicate  film  of  copper 
ferrocyanide  forms  where  the  two  liquids  come  into  contact. 
The  student  can  see  this  very  effectively  by  performing  the 
following  experiment. 


42  OSMOTIC  PRESSURE 

Experiment — Let  a  drop  of  a  cold  saturated  potassium  f erro- 
cyanide  solution  run  from  a  fine  glass  capillary  into  a  0-5 
molar  solution  of  copper  sulphate  contained  in  a  glass  vessel. 
Detach  the  drop  by  a  slight  motion  of  the  tube  so  that  it  sinks 
to  the  bottom  of  the  vessel.  The  drop  at  the  moment  of  its 
entrance  into  the  solution  became  surrounded  with  a  thin  film 
of  cupric  ferrocyanide,  which  keeps  growing  in  thickness  at 
the  expense  of  the  dissolved  components.  The  concentration 
of  the  solute  within  the  membrane  is  greater  than  that 
of  the  copper  sulphate  outside,  hence  water  passes  into  the 
globule  and  the  membrane  expands,  because  of  the  pressure 
caused  by  the  entrance  of  the  water  through  the  walls.  The 
membrane  is  at  first  transparent  and  traversed  by  brown 
veins.  As  the  expansion  of  the  cell  continues,  the  specific 
gravity  of  the  contents  diminishes  until  it  becomes  less 
than  the  copper  sulphate  solution  ;  then  the  cell  rises  to 
the  surface  of  the  solution.  In  time,  however,  the  walls 
become  sufficiently  thick  to  cause  the  cell  once  more  to  sink 
to  the  bottom,  where  it  remains  permanently. 

The  copper  ferrocyanide  film,  however,  is  very  delicate,  and, 
to  be  of  any  practical  value,  has  to  be  supported.  This  is  most 
conveniently  done  by  precipitating  the  copper  ferrocyanide 
within  the  walls  of  an  unglazed  porcelain  vessel.  By  this 
means  an  area  of  film  which  can  be  utilized  is  obtained.  In 
reality  it  is  built  up  of  a  very  large  number  of  very  small 
films,  each  of  which  is  supported  by  the  porcelain  particles 
round  it.  The  membrane  thus  obtained  is  almost  completely 
unpermeable  to  a  great  many  solutions,  and  for  our  purpose  be 
regarded  as  a  true  semipermeable  membrane. 

Preparation  of  a  Semipermeable  Membrane — Take  an  unglazed 
porcelain  pot  8  or  10  cms.  high  and  2  to  f  cms.  diameter.  Soak 
it  in  water  for  several  hours,  then  fill  up  the  pot  to  near  the 
top  with  a  solution  of  copper  sulphate  containing  2-5  grams 
per  litre,  immerse  this  in  a  beaker  containing  a  solution  of 
potassium  ferrocyanide  of  a  strength  2-1  grams  per  litre,  so  that 
the  levels  of  the  liquid,  both  inside  and  outside  the  pot,  are 
about  equal.  Allow  to  stand  for  several  hours.  The  salts 
diffuse  through  the  walls,  and  where  they  meet  a  copper  ferro- 
cyanide membrane  is  formed,  which,  since  it  is  impermeable 
to  the  salts  from  which  it  is  formed  remains  quite  thin,  but  is 
capable  of  withstanding  fairly  large  pressures  since  it  is  sup- 
ported by  the  walls  of  the  porous  pot.  The  porous  pot  is  then 
taken  out  and  thoroughly  washed. 


DETERMINATION  OF  OSMOTIC  PRESSURE 


Experimental  Determination  of  Osmotic  Pressure — A  suitable 
form  of  apparatus  is  shown  in  Fig.  26.  A  tube  B,  of  such  a 
diameter  that  as  near  as  possible  it  just  fits  inside  the  porous 
pot,  is  fixed  to  the  porous  pot  by  surrounding  the  junction 
with  a  glass  collar,  C,  the  whole  being  held  in  position  by 
filling  the  surrounding  space  with  cement  or  sealing-wax,  the 
joint  being  perfectly  air-tight.  The 
top  of  the  tube  B  is  closed  by  a 
stopper,  through  which  passes  a 
glass  tube  E,  which  is  drawn  out 
at  the  end.  To  the  side  tube  F 
is  attached  a  graduated  manometer, 
provided  with  a  reservoir  bulb,  H. 

Experimental  Determination  of  the 
Osmotic  Pressure  of  Cane  Sugar  Solu- 
tion— Fit  up  the  apparatus  as  previ- 
ously described.  Prepare  a  1  per 
cent,  solution  of  cane  sugar,  and  fill 
up  the  porous  pot  to  near  the  top 
by  removing  cork  E.  Then  attach 
the  manometer  and  make  joints  E 
and  F  perfectly  air-tight  by  coating 
the  junctions  of  the  stoppers  with 
the  glass  with  a  layer  of  some 
suitable  cement  or  sealing-wax.  The 
tube  E  has  up  to  now  been  open  to 
the  air,  thus  preserving  atmospheric 
pressure  throughout  the  apparatus 
until  all  joints  were  tight— i.e.,  the 
mercury  in  the  manometer  is  the 
same  in  both  limbs.  Now  seal  off  E 
in  a  blowpipe  (note  E  has  been 

already  drawn  out  to  a  fine  point,  so  that  the  sealing  off  is 
only  a  matter  of  a  second  or  so),  and  note  carefully  the  mano- 
meter reading.  Now  immerse  the  porous  pot  in  a  beaker  of 
distilled  water  at  room  temperature.  Water  gradually  passes 
into  the  cell,  and  the  air  in  the  upper  part  of  the  apparatus 
is  compressed,  and  thus  drives  up  the  mercury  in  the  mano- 
meter, thus  measuring  the  pressure  inside  the  cell.  Take 
readings  every  hour,  then  allow  to  stand  over  night,  and  take 
readings  again  until  no  alteration  occurs.  The  actual  time 
required  depends  upon  the  particular  cell.  If  the  cell  has 


FIG.  26 


44  OSMOTIC  PRESSURE 

been  well  prepared,  the  maximum  pressure  will  be  retained  for 
several  days.  Make  a  note  of  the  maximum  pressure. 
According  to  Pfeffer  the  osmotic  pressure  of  a  1  per  cent, 
solution  of  cane  sugar  is  535  mm.  of  mercury. 

For  higher  concentrations  the  osmotic  pressure  of  cane 
sugar  solutions  rises  to  considerably  more  than  an  atmosphere, 
and  a  manometer  of  the  closed  type  has  to  be  used — for 
example,  a  6  per  cent,  solution  of  cane  sugar  has  an  osmotic 
pressure  of  3075  mm.  of  mercury  at  room  temperature. 

Osmotic  pressure  measurements  do  not  make  suitable 
laboratory  exercises,  but  students  ought  to  be  familiar  with 
the  method  by  performing  the  experiment  described  above. 
The  apparatus  once  set  up,  other  experiments  may  be  done 
while  equilibrium  is  being  established.  Where  necessary,  five 
or  six  students  may  take  readings  from  one  apparatus. 

The  following  laws  relating  to  osmotic  pressure  have  been 
established : 

1.  Temperature  and  concentration  being  the  same,  different 
substances,  when  in  solution,  exert  different  pressures. 

2.  For  one  and  the  same  substance,  at  constant  temperature, 
the    pressure    exerted    is    proportional    to    the    concentra- 
tion. 

3.  The  pressure  for  a  solution  of  a  given   concentration 
is  proportional  to  the  absolute  temperature,  the  volume  being 
kept  constant. 

4.  Equimolecular  quantities  of  different  substances,  when 
dissolved  in  the  same  volume  of  solvent,  exert  equal  pressures 
under  the  same  conditions  of  temperature  and  pressure. 

Note — This  is  only  true  of  those  substances  whose  mole- 
cules neither  dissociate  into  simple  forms  (i.e.,  non-electro- 
lytes), nor  associate  into  more  complex  molecules  when  in 
solution. 

It  will  be  observed  that  the  second  statement  is  analogous 
to  Boyle's  law ;  the  third  corresponds  to  Charles's  law ; 
while  the  last  is  an  extension  of  Avagadro's  hypothesis. 
Hence  Van't  Hoff  came  to  the  following  conclusion  : 

"  The  osmotic  pressure  exerted  by  any  substance  in  solution 
is  the  same  as  it  would  exert  if  present  as  a  gas  in  the  same 
volume  as  that  occupied  by  the  solution,  provided  that  the 
solution  is  so  dilute  that  the  volume  occupied  by  the  solute 
is  negligible  in  comparison  with  that  occupied  by  the 
solvent." 


DETERMINATION  OF  OSMOTIC  PRESSURE 
EXAMPLES  FROM  PFEFFER'S  RESULTS 


45 


Percentage  of 
Sugar  in  Solution 

Osmotic  Pressure 
in  Mm.  of 
Mercury  =  P. 

Volume  of  Solution 
containing  1  Gram 
of  Sugar  =V. 

P.V. 

C.c. 

1 

535 

99-6 

53286 

2 

1016 

49-6 

50394 

4 

2082 

24-61 

51238 

6 

3075 

16-34 

50245 

CHAPTER  VIII 
REFRACTIVITY  MEASUREMENTS 

Refractive  Index— When  a  ray  of  light  passes  from  one 
medium  to  another,  and  the  densities  of  the  two  mediums  are 

different,  the  direction  of  the 
ray  is  altered,  except  when  the 
ray   is    perpendicular   to   the 
boundary   between    the    two 
media,  in  which  case  no  change 
occurs.    This  latter  position  is 
—     called  the    normal.     Consider 
Fig.  27.     Let  A  and  B  repre- 
sent the  two  media  where  B 
is  denser  than  A,  also  let  a — b 
represent  the  normal,  then  a 
ray  of  light  passing  through  A 
at  an  angle  "  i"  to  a — b  will 
be    deflected   on   entering   B 
in  such  a  manner  that  angle 
"e"  is  less  than  angle  "i."     In    other  words   the  angle  of 
incidence,  "i,"  will  be  greater  than  the  angle  of  refraction,  "e." 
The  relation  between  these  two  angles  is  termed  the  refrac- 
tive index,  and  further  it  can  be  shown  that — 

sin  i  _  N 
sin  e~~  n' 

where  N  is  the  refractive  index  in  the  denser  medium,  and  n 
the  refractive  index  of  the  less  dense  medium. 

It  will  be  seen  that  the  maximum  value  for  i  is  90°,  in 
which  case  sin  i  =  1 ;  then — 

n 
sin  £  =  Tr. 


b 

FIG.  27 


46 


REFRACTIVE  INDEX 


47 


Determination  of  the  Refractive  Index  of  a  Liquid — The 
principle  indicated  above  is  used  in  determining  the  refractive 
index  of  a  liquid,  the  index  of  refraction  being  found  by 
comparison  with  a  glass  prism  of  known  refractive  index, 
which  must  be  greater  than  that  of  the  liquid. 

In  actual  practice  monochromatic  light  is  used,  since  white 
light  would  give  spectrum  effects,  thereby  preventing  the 
obtaining  of  sharp  and  definite  images.  Consider  Fig.  28, 
which  represents  a  glass  cell  containing  the  liquid  to  be 
examined,  mounted  on  a  right-angled  glass  prism  of  refractive 


N 


N 


FIG.  28 


FIG.  29 


index,  N.  Then  a  ray  of  light  (Fig.  28)  entering  at  A  will 
have  a  path  somewhat  as  indicated,  and  the  relation 

sin  e'     N 

— =  —   exists,     ouppose   now   the   angle   e    is    gradually 

sin  e      n 

increased  :  a  point  is  reached  when  no  light  is  visible  at  B, 
this  occurs  when  angle  e'  becomes  90°.  At  this  point  the 
light  is  totally  reflected.  The  ray  of  light  is  entering  horizon- 
tally, as  shown  in  Fig.  29,  and  in  actual  practice  it  is  the 
position  at  which  this  occurs  that  is  determined.  Thus, 
when  e'  =  90°  we  have — 

n 

Sin  e  =  TTn 


n  being  the  refractive  index  of  the  liquid,  and  N  that  of  the 
prism. 


48  REFRACTIVITY  MEASUREMENTS 

Further,  N=  ^^ 

sin  i" 

But  sin  e  =  cos  i ; 


n 
•••cos*  =  j^ 


— i.e., 


n  =  cos  i  N. 


FIG.  30 


SPECIFIC  AND  MOLECULAR  REFRACT1VITY          49 

But  cos2  i  =  1  —  sin2  *  ; 


sn   *. 


Substituting  SH      for  sin2  i, 


we  get  n  =  JN2  -  sin2  i'. 

Hence  we  see  that  to  find  n  we  have  to  determine  the  value 
of  i'  when  the  incident  ray  is  horizontal.  In  actual  practice  it 
is  not  usually  necessary  to  go  through  the  above  calculation, 
since  the  makers  supply  tables  giving  values  of  n  for  each 
value  of  i'. 

Specific  and  Molecular  Refractivity — The  refractive  index 
varies  with  the  temperature  of  the  liquid,  and  according  to 

Gladstone  and  Dale  —3—  =  constant,  where  d  is  the  density  of 
the  liquid  ;  Lorentz  and  Lorenz,  however,  find  the  expression 

712-1       1 

y  2.0  '  ~d  giyes  a  better  constant.  The  value  of  this  expres- 
sion is  termed  the  specific  refractivity  of  the  liquid.  This 
value  is  dependent  only  on  the  nature  of  the  liquid,  and  is  a 
characteristic  property  of  it. 

Molecular  Refractivity  is  found  by  multiplying  this  value  by 

the  molecular  weight  of  the  substance.       2 — ^  •  -y-  gives   a 

constant,  where  M  is  the  molecular  weight  of  the  substance. 

Method  of  Determination  of  the  Refractive  Index — The  best 
instrument  to  use  for  this  purpose  is  the  Pulfrich  refracto- 
meter,  which  is  somewhat  as  shown  in  Fig.  30. 

L  is  a  refracting  prism,  on  which  is  mounted  a  glass  cell ; 
this  is  clamped  in  position  by  the  screw  K,  so  that  the  flat  face  of 
the  prism  faces  the  telescope  F.  Since  a  constant  temperature 
is  required,  the  temperature  of  the  liquid  in  the  cell  is  con- 
trolled by  heater  S  (see  section,  Fig.  31),  through  which  water 
from  a  thermostat  is  circulated.  A  thermometer  screwed 
into  the  heater  indicates  the  actual  temperature  inside  the 
cell.  At  the  end  of  the  telescope  nearest  to  the  prism  is  a  cap, 
in  which  is  an  oblong  slit,  through  which  the  light  passes  after 
refraction.  With  a  single  cell  the  whole  slit  is  used,  but  with 
a  divided  cell  half  the  slit  is  used. 


50 


REFRACTIVITY  MEASUREMENTS 


Near  the  eyepiece  end  of  the  telescope  is  a  large  graduated 
metal  disc,  Z>,  which  is  graduated  in  degrees  and  half -degrees. 
A  vernier  is  also  provided,  by  means  of  which  a  single  minute 

can  be  read  off.  This  vernier  read- 
ing is  made  by  the  aid  of  a 
telescope,  which  can  be  rotated 
round  the  disc.  To  make  the  final 
adjustment  the  disc  is  fixed  by 
screw  H,  and  the  fine  adjustment 
made  by  means  of  screw  0. 

N  is  a  reflecting  prism  on  a 
movable  arm,  and  P  is  a  lens  by 
means  of  which  the  light  can  be 
focussed  on  to  the  centre  of  the 
cell.  In  any  experiment  it  is 
essential  that  the  ray  of  light 
should  be  monochromatic  and  of  a 
definite  wave  length.  There  are 
three  spectrum  lines,  which  are 
generally  used  for  this  purpose. 
D  line  (given  by  sodium  flame), 
C  line  (red  line  of  the  hydrogen 
spectrum),  and  the  F  line  (the  blue 
line  of  the  hydrogen  spectrum). 
The  D  line  is  obtained,  say,  from 
sodium  chloride  in  a  bunsen  flame, 
C  and  F  lines  are  obtained  from 
Geisler  tubes. 

Determination  of  the  Zero- Point 
— A  small  right  angle  prism  is  let 

in  the  telescope  tube  near  the  eyepiece  for  the  purpose 
of  determining  the  zero  of  the  instrument.  This  prism  is 
illuminated  by  some  strong  source  of  light,  such  as  an  electric 
lamp.  This  light  is  reflected  along  the  telescope.  Here  it 
emerges  through  the  slit  at  the  other  end  and  strikes  the  face 
of  the  prism,  thereby  being  reflected  back  along  the  telescope. 
Hence,  on  looking  through  the  eyepiece,  the  small  prism,  and 
also  an  image  of  it,  are  seen  on  the  right  and  left  of  the  field 
of  view  respectively.  On  the  image  are  seen  two  dark  lines 
running  parallel  to  the  cross  wires;  these  are  the  reflected 
images  of  the  cross  wires  (see  Fig.  32).  Rotate  the  graduated 
disc  until  the  cross  wires  and  their  images  coincide  as  near  as 


FIG.  31 


SPECIFIC  AND  MOLECULAR  REFRACTIVITY          51 

possible.     Tighten  screw  H,  and  make  the  final  adjustment  by 
means  of  screw  G- 

Now  observe  the  vernier  reading,  and  the  difference  of  this 
from  zero  is  the  correction  which  has  to  be  applied  to  every 
subsequent  reading. 

It  sometimes  happens  that  the  simultaneous  coincidence  of 
the  cross  wires  with  their  images  cannot  be  obtained.  In 
this  case  the  true  zero  is  obtained  by  taking 
the  reading  when  the  upper  wire  coincides 
with  the  upper  image,  and  again  when 
the  lower  wire  coincides  with  the  lower 
image,  and  then  taking  the  mean  of  the 
two  readings.  The  drum  on  the  fine 
adjustment  screw  is  divided  into  200 
divisions,  and  moves  along  a  horizontal  FIG.  32 

scale,  which  is  divided  into  degrees  and 
thirds  of  a  degree.     One  complete  turn  of  the  drum  corre- 
sponds to  a  third  of  a  degree  (20'),  therefore  one  division  on 
the  drum  is  equal  to  0-1'. 

Experimental  Determination  of  the  Refractive  Index  of  Alcohol 
for  D  line — The  sodium  flame  is  placed  about  2  feet  from  the 
reflecting  prism  N,  which  must  be  arranged  so  as  to  throw  an 
image  of  the  flame  on  the  cell  which  is  mounted  on  the  re- 
fracting prism.  Usually  a  wooden  cap,  W,  with  a  side  slit,  is 
placed  over  the  cell  to  exclude  extraneous  light ;  it  also  serves 
to  keep  the  temperature  constant. 

Introduce  a  layer  of  alcohol  about  5  mm.  deep  by  means 
of  a  pipette,  taking  care  not  to  touch  the  polished  surface 
of  the  prism.  Now  bring  into  position  the  heater,  lower- 
ing the  movable  flange  until  it  is  in  contact  with  the  top  of 
the  cell.  Circulate  the  water  from  the  thermostat  at  25°  C. 
through  the  heater,  and  when  the  temperature  becomes  con- 
stant to  0'1°,  a  measurement  may  be  made. 

Rotate  the  graduated  disc  until  a  bright  yellow  band  crosses 
the  field  of  view.  Then  clamp  it  by  means  of  screw  H,  and 
then  by  means  of  screw  G  arrange  the  intersection  of  the  cross 
wire  on  the  upper  edge  of  the  yellow  band.  The  reading  then 
gives  the  angle  of  emergence,  from  which  the  index  of  refrac- 
tion can  be  obtained  from  the  tables. 

The  tables  are  usually  divided  into  six  columns ;  if  is  the 
angle  of  immergence  obtained  as  above,  nv  is  the  value  calcu- 
lated from  n=  VN2  -  sin2  *',  &»  is  the  amount  in  units  to  be 


52 


REFRACTJVITY  MEASUREMENTS 


subtracted  from  the  last  decimal  place  for  a  rise  1'  in  the  value 
of  i. 

The  last  three  columns  are  corrections  when  C,  F,  G  lines  are 
used.  Having  obtained  the  refractive  index  n,  the  specific 
refradivity  can  be  calculated  from  the  formula  of  either  Glad- 
stone and  Dale  — j-  =  R,  where  R  is  the  specific  ref ractivity, 
or  that  of  Lorentz  and  Lorenz,  in  which  case — 

2        11 
E-j^gy 

the  value  of  d  being  obtained  either  from  tables,  or  directly 
by  the  method  given  for  the  determination  of  the  density  of 
liquids. 

The  molecular  refradivity  will  be — 


MR: 


MandMR  = 


respectively,  where  M  is  the  molecular  weight  of  the  liquid. 

It  has  been  found  from  measurements  on  a  large  number  of 
organic  liquids  that  the  molecular  refraction  may  be  repre- 
sented as  an  approximate  summation  of  the  atomic  refractivi- 
ties,  so  that  the  refractive  power  is  largely  an  additive 
property. 

The  values  given  for  n  in  the  tables  are  usually  for  a  tem- 
perature of  20°  C.,  so  that  if  the  experiment  is  done  at  25°,  it 
is  necessary  to  make  a  correction.  This  correction  will  be 
found  in  another  table. 

CORRECTION  FOR  TEMPERATURE,  THE  UNITS  TO  BE  ADDED 
TO  THE  FIFTH  DECIMAL  PLACE 


n 

C 

D 

F 

1-60 

0-25 

0-29 

0-40 

1-50 

0-26 

0-30 

0-42 

1-40 

0-28 

0-33 

0-45 

1  30 

0-30 

0-35 

0-49 

The  value  in  second,  third,  and  fourth  columns  are  the  cor- 
rectness to  be  applied  per  degree  for  the  spectrum  lines  C,  D,  F 


SPECIFIC  AND  MOLECULAR  REFRACTIVITY          53 

respectively.  The  first  column  n  is  the  value  obtained  from 
the  value  of  i  in  actual  experiment  given  for  20°. 

Suppose  an  experiment  at  25°  using  D  light  gave  a  value  of 
n  1-53107,  then  the  correction  would  be  (25  -  20)  x  0-30=  1-5. 
This  has  to  be  added  to  the  fifth  decimal  place  of  the  original 
value  of  n,  hence  nD  (at  25°)=  1-531085. 

Exercise — Given  the  following  atomic  refractivities  for  D 
line  :  0  =  2-501,  H  =  1-051,  0  (in  OH)=  1-521. 

Compare  the  molecular  refractivity  calculated  from  the 
above  with  that  obtained  in  actual  experiment. 

When  hydrogen  lines  are  used,  the  reflecting  prism  is  not 
required.  The  Geissler  tube  is  clamped  in  position  and  the 
beam  of  light  focussed  by  means  of  lens  P  on  to  the  slit  in  the 
wooden  cap  over  the  cell.  The  visible  lines  may  be  made  sharp 
by  means  of  a  diaphragm  fitted  on  to  the  lens.  On  looking 
through  the  telescope  the  chief  lines  visible  are  on  the  extreme 
right,  the  red  line  C,  a  pale  blue  line  F ;  and  on  the  extreme 
left  two  violet  lines,  G',  and  G" ;  other  lines  (green)  are  usually 
also  visible,  due  to  mercury  vapour.  Only  C  and  F  lines  are 
used  experimentally.  The  values  of  i'  are  determined  for  C 
and  F  separately  by  arranging  the  intersection  of  the  cross 
wires  on  the  upper  edge  of  the  respective  lines. 

Having  fixed  the  graduated  disc  force  for,  say,  line  C,  the 
measurement  for  F  can  be  made  by  means  of  the  fine  adjust- 
ment G. 

Experiment  to  Determine  the  Refractive  Index  of  Acetone  for  C 
and  F  Lines — On  examining  the  tables  it  will  be  observed 
that  corrections  have  to  be  made  for  C  and  F  lines,  in  units 
of  the  fifth  decimal  place.  Example,  where  the  correction  is 
given,  0-589,  the  correction  to  be  made  is  0-00589. 

In  the  case  C  line  the  correction  must  be  subtracted  from  the 
value  of  WD. 

In  the  case  of  F  (or  G')  line  the  correction  value  must  be 
added  to  the  value  of  WD  (the  values  of  n  for  D,  C,  and  F  lines 
respectively  are  usually  indicated  thus :  n^  nc,  TIF). 

Note — Whether  the  correction  is  added  or  subtracted  from 
the  value  for  %,  depends  on  the  relative  positions  of  C  and  F 
lines  with  respect  to  D  in  the  spectrum. 

Refractivity  of  Substances  in  Solution — The  refractivity  of 
a  soluble  substance  can  be  determined  from  the  refractivity  of 
its  solution  and  solvent,  provided  the  solution  is  not  too 
strong. 


54  REFRACTIVITY  MEASUREMENTS 

Let  %,  n2,  nB  be  the  refractive  indices  of  the  solute,  solvent, 
and  solution  respectively ;  and  dv  d2,  d3  the  corresponding 
densities,  and  x  the  percentage  of  solute  in  solution. 

Then  using  Lorentz  and  Lorenz  formula — 

ni2 1_l    1  =  100  V-l     I     n*  -  1    _!_    100 -a; 

wx2  +  2  '  dt  ~   x    w32  +  2    ds  ~  n2 '  \  2  '  dz         x 

or  Gladstone  and  Dale's  formula,  we  get — 

AI 

Experiment  to  Determine  the  Molecular  Refr activity  of  Sodium 
Chloride — Make  up  a  10  per  cent,  solution,  and  first  determine 
its  density  at  25°  relative  to  water  at  25°. 

Then  determine  the  refractive  index  of  pure  water  and 
solution  respectively  for  the  D  line  at  25°.  Calculate  the 
specific  and  molecular  refractivities  of  sodium  chloride,  using 
Gladstone  and  Dale  formula. 


CHAPTER  IX 
ROTATION  OF  THE  PLANE  OF  POLARIZATION 

THE  ref  ractivity  of  liquids  and  dissolved  substances  is  general ; 
but  when  we  come  to  the  polarization  of  light,  we  are  dealing 
with  a  property  possessed  only  by  comparatively  few  liquids 
and  dissolved  substances.  This  property  depends  entirely  on 
the  arrangement  of  the  atoms  in  the  molecule — for  example, 
isorneric  substances  have  usually  very  similar  refractive  pro- 
perties, but  it  often  happens  that  they  behave  very  differently 
with  respect  to  polarized  light. 

Polarized  light  (light  in  which  the  vibrations  lie  all  in  one 
plane)  is  obtained  by  passing  monochromatic  light  through  a 
Nicol  prism  (or  tourmaline  plate),  which  cuts  off  all  rays 
except  those  vibrating  in  one  plane.  This  prism  is  termed  the 
polarizer.  The  light  then  passes  on,  and  is  examined  by  a 
second  Nicol  prism,  termed  the  analyzer. 

When  these  two  prisms  have  their  axes  at  right  angles,  the 
field  of  view  is  totally  dark.  If  when  such  conditions  exist  a 
tube  containing  cane  sugar  solution  be  interposed,  the  field 
becomes  illuminated,  but  it  becomes  dark  again  on  rotating 
the  polarizer  through  a  certain  angle.  What  has  happened  is, 
the  plane  polarization  has  been  twisted  through  a  certain 
angle  by  the  cane  sugar  solution.  The  analyzer  has  therefore 
to  be  turned  through  a  certain  angle,  in  order  to  take  up 
the  previous  position  relative  to  the  plane  of  polarized 
light. 

The  actual  angle  depends  on  the  nature  of  the  liquid,  on 
the  wave  length  of  the  light  used  in  the  measurements  and  on 
the  temperature,  and  is  proportional  to  the  length  of  the  tube 
containing  the  liquid  under  examination. 

Specific  rotation  is  defined  as  the  angle  of  rotation  produced  by  a 
liquid,  which  in  a  volume  of  1  c.c.  contains  1  gram  of  active  sid)- 

55 


56       ROTATION  OF  THE  PLANE  OF  POLARIZATION 

stance,  when  the  length  of  the  column  is  1  dcm.,  and  is  represented 
thus  — 


where  a  is  the  observed  angle,  I  is  the  length  of  the  column  in 
decimetres,  d  is  the  density  of  the  liquid  at  temperature  t  ; 
D  indicates  that  sodium  light  was  used  as  a  source  of  illumina- 
tion. For  solutions  the  specific  rotation  is  — 


lOOa 


where  x  is  the  number  of  grams  of  solute  in  100  grams  of 
solution. 

Polarimeter — The  types  now  largely  in  use  are  those 
designed  by  Lippich  and  Laurent.  The  two  forms  only  differ 
in  the  mode  of  production  of  the  half-shadow.  The  sodium 
light  enters  through  a  diaphragm,  which  is  provided  with  a 
plate  (or  solution)  of  a  crystal  of  potassium  bichromate,  which 
filters  out  any  extraneous  light  which  accompanies  the  yellow 
light. 

On  leaving  the  lens  E  the  rays  pass  parallel  into  the  Nicol 
prism  Z),  and  then  enters  the  second  diaphragm,  F,  half  of 

In  G)  ^  EH  tn  9  \z\  o ! 

IH        I         G  P  F      D     E  ' 

FIG.  33 

which  is  covered  with  a  quartz  or  mica  plate  of  definite  thick- 
ness, and  cut  parallel  to  the  axis.  From  here  the  rays  pass 
through  the  liquid  tube  P  into  the  analyzer  G,  and  then 
through  the  lenses  1  and  H  of  the  telescope  through  which 
the  observations  are  made  (see  Fig.  :33). 

The  characteristic  part  of  the  apparatus  is  the  quartz  or 
mica  plate,  the  thickness  of  which  is  chosen  so  that  the  rays 
of  sodium  light  which  passes  through  suffers  a  change  of  phase 
of  half  a  wave  length,  but  still  remains  plane  polarized.  Thus 
we  have  two  beams  of  polarized  light,  one  double  the  wave 
length  of  the  other.  If  the  polarizer  is  adjusted  so  that  the 
plane  of  polarization  of  light  is  parallel  to  the  axis  of  the 


POLARIZATION 


57 


quartz,  then  for  each  position  of  the  analyzer  the  two  halves 
of  the  field  of  view  will  be  equally  illuminated.  If,  however, 
the  polarizer  is  placed  at  an  angle  with  this  axis,  the  plane  of 
polarization  of  the  rays  of  light  which  pass  through  the 
quartz  plate  will  suffer  a  like  displacement,  but  in  the  opposite 
direction. 


m 


FIG.  34 

When  such  conditions  exist,  the  circular  field  appears  divided 
into  two  halves,  which  are,  with  two  exceptions,  unequally 
illuminated.  For  two  positions,  however,  180°  apart,  both 
halves  are  equally  illuminated.  The  apparatus  (see  Fig.  34) 
is  so  constructed  that  the  analyzer,  fastened  to  the  telescope 
and  vernier  n,  can  be  moved  by  means  of  an  arm,  T,  on  a 
fixed  circle,  K;  the  vernier  can  be  read  by  means  of  a 
telescope. 

As  already  mentioned,  the  plane  of  the  polarizer  must  form 
an  angle  with  the  axis  of  the  quartz  plate,  thereby  producing 
unequal  illuminations  of  the  two  halves  of  the  field.  This  is 


58   ROTATION  OF  THE  PLANE  OF  POLARIZATION 

accomplished  by  means  of  a  contrivance,  h,  by  means  of  which 
the  polarizer  can  be  rotated.  The  apparatus  is  first  adjusted 
to  the  parallel  position,  so  that  for  any  position  of  the  analyzer 
the  two  halves  of  the  field  view  are  equally  illuminated.  The 
polarizer  is  then  rotated  through  an  angle,  6,  by  means  of  h 
(see  note).  The  smaller  the  angle  is,  the  more  sensitive  is  the 
instrument ;  the  more  brilliant  the  light  and  the  clearer  the 
liquid,  the  smaller  0  can  be  made.  The  proper  adjustment  of 
the  polarizer  is  that  position  corresponding  to  the  greatest 
change  of  the  shade  in  the  field  of  view  for  a  slight  movement 
of  the  analyzer. 

At  the  beginning  of  an  experiment  the  telescope  F  is 
focussed  sharply  on  the  diaphragm,  so  that  the  dividing  line 
at  the  edge  of  the  quartz  plate  appears  quite  sharp. 

In  determining  the  zero-point  the  tube  should  be  filled  with 
distilled  water,  in  order  that  the  intensity  of  the  light  may  be 
the  same  as  when  the  active  liquid  is  observed.  In  case  the 
field  of  view  is  too  dark,  on  account  of  the  liquid  being 
coloured  or  not  clear,  the  illumination  may  be  increased  by  a 
slight  rotation  of  the  polarizer;  this,  however,  as  before 
mentioned,  renders  the  instrument  less  sensitive. 

The  angle  6  through  which  the  polarizer  is  rotated  is 
called  the  half -shadow  angle. 

Since  the  quartz  disc  is  fixed,  only  one  wave  length  of  light 
can  be  used  with  any  one  instrument,  and  the  quartz  disc 
being  definitely  gauged  to  just  half  this  wave  length. 

The  apparatus  described  above  is  the  Laurent  type.  The 
Lippich  differs  in  that  the  quartz  plate  is  replaced  by  a  third 
Nicol  prism,  which  covers  half  the  field  of  view.  This  appar- 
atus has  the  advantage  over  the  Laurent  type,  in  that  homo- 
geneous light  of  any  wave  length  can  be  used. 

The  observation  tubes  in  which  the  liquid  is  placed  usually 
consists  of  a  thick- walled  glass  tube,  with  accurately  ground 
ends  closed  by  circular  glass  plates.  These  plates  are  held  in 
position  by  means  of  screw  caps.  The  tubes  are  either  1  dcm. 
in  length,  or  some  simple  multiple  of  a  decimetre. 

In  constant  temperature  experiments  the  tube  is  surrounded 
with  an  outer  jacket,  through  which  water  from  a  thermostat 
can  be  circulated  (see  Figs.  35,  36). 

Experiment  to  Determine  the  Specific  Rotation  of  Cane  Sugar — 
Dissolve  10  grams  of  cane  sugar  in  a  little  water  and  make  up 
to  100  c.c.  Then,  having  determined  the  zero  with  distilled 


POLARIZATION 


59 


water  in  the  observation  tube,  fill  up  the  tube  completely  (free 
from  air  bubbles)  with  cane  sugar  solution  (first  wash  the  tube 
out  with  the  solution).  Then  determine  the  angle  of  rotation 
— i.e.,  redetermine  the  position  of  equal  illumination.  Then 
from  this  angle  calculate  the  specific  rotation.  For  accurate 
experiments  ;a  jacket  tube  should  be  used,  through  which 
water  is  circulated  from  a  thermostat.  For  ordinary  purposes 
the  temperature  of  the  room  is  sufficiently  constant. 


FIG.  35 


FIG.  36 


To  Determine  the  Amount  of  Pure  Cane  Sugar  in  a  Sample  of 
Sugar — The  sugar  will  contain  mainly  cane  sugar  and  a  small 
amount  of  invert  sugar,  also  traces  of  optically  inactive  sub- 
stances which  do  not  materially  affect  the  experiment. 

Weigh  out  the  two  samples  of  sugar,  each  10  grams  weight. 
One  sample  dissolve  in  distilled  water,  and  make  up  to  100  c.c. 
The  other  dissolve  in  about  50  c.c.  of  water,  add  10  c.c.  of 
strong  hydrochloric  acid,  and  heat  up  to  about  70°  for  ten  to 
fifteen  minutes,  and  then  make  up  to  100  c.c.  Now  deter- 
mine the  angle  of  rotation  of  each  sample  separately.  In  the 
first  case  the  value  will  be  for  impure  cane  sugar,  and  in  the 
second  case  for  invert  sugar  only. 


60      ROTATION  OF  THE  PLANE  OF  POLARIZATION 

For  cane  sugar — 

[a]«j-  66-5  -0-0184(i?  -20). 
For  invert  sugar — 

[a]^  =  - 19-66  -  0-0361  C'  -  0-304(£  -  20). 

The  influence  of  concentration  is  greater  in  the  second  case, 
and  has  therefore  to  be  taken  into  consideration  (C'). 

Suppose  C  grams  of  cane  sugar  in  the  sample.  Then  C' 
grams  of  invert  sugar  result ;  then — 

C/_360C 
since — 

If  a'  is  the  angle  after  inversion — 

a'=  -  {19-66  +  0-0361C'-  0-304(i?-  20)}  yj^  +  A 

CY 
a=  {66-5 -0-0184(i?- 20)}  ^Q  + A 

where  a  is  the  angle  of  the  original  solution,  and  (3  the  angle 
due  to  the  presence  of  impurity  (invert  sugar)  in  the  initial 
sugar,  t  is  the  temperature  of  experiment,  then — 

[/"*1  7  — ^ 

YOO  {66-5 -0-01 84(i? -20)}     + 

r  r'/n 

{19-66  + 0-0361  C'- 0-304(i?- 20)}  y^Q   • 
Substituting  C'  =  ~  C,  we  get— 


rv 

«  -  of  =  iQQ[{66-5  -  0-0184(^  -  20)}  + 

{19-66  +  0-0380  C  -  0-304^  -  20)}  1-0526], 

from  which  C  can  be  calculated,  and  hence  C'. 

Note — The  action  of  the  quartz  plate  may  be  explained  as 
follows  : 

The  plane  of  polarized  light  falling  on  the  plate  is  decom- 
posed into  two  rays.  The  two  rays  traverse  the  plate  with 


POLARIZATION 


61 


different  velocities,  and  the  thickness  of  the  plate  is  so  arranged 
that  a  difference  in  phase  of  half  a  wave  length  is  produced. 
The  effect  of  this  is,  that  if  the  light  passing  through  the  un- 
covered portion  of  the  field  polarized  in  direction  0  B,  making 
an  angle  6  with  0  A  (the  edge  of  the  quartz  plate),  then  that 
which  has  passed  through  the  plate  is  polarized  in  a  direction 


FIG.  37 

0  B',  so  that  B  0  A  =  A  0  Bf.  On  looking  through  the  eye- 
piece the  two  halves  of  the  field  will  be  unequally  illuminated, 
unless  the  principal  plane  of  the  analyzing  Nicol  in  the  eye- 
piece make  equal  angles  with  0  B  and  0  B' — i.e.,  is  parallel 
to  or  perpendicular  to  0  A.  In  the  former  case  the  field  will 
be  equally  bright,  in  the  latter  equally  dark  (see  Fig.  37). 


CHAPTER  X 
SPECTRUM  ANALYSIS 

THE  spectroscope,  next  to  the  balance,  is  the  most  im- 
portant instrument  of  the  chemist.  By  its  aid  a  chemist  is 
able  to  identify  substances  which  heretofore  were  entirely 
beyond  his  ken.  It  has  long  been  known  that  certain 
chemical  substances,  when  strongly  heated  in  the  almost 
colourless  flame  of  a  bunsen  or  blowpipe,  impart  a  charac- 
teristic colour  to  the  flame.  For  example,  sodium  salts  colour 
the  flame  intense  yellow,  while  potassium  salts  impart  a  violet 
colour  to  the  flame.  If,  however,  sodium  and  potassium  are 
present  in  the  same  substance,  then  the  intensity  of  the  sodium 
yellow  completely  masks  the  violet  of  the  potassium.  Hence 
by  this  method  it  is  impossible  to  detect  potassium  in  pres- 
ence of  sodium  with  the  naked  eye.  This  difficulty  is  over- 
come by  regarding  the  flame  through  a  prism  instead  of  with 
the  naked  eye.  By  this  means  the  light  is  refracted,  each 
differently  coloured  ray  having  its  own  specific  refractivity. 
If  the  source  of  light  be  white,  then  a  continuous  band  of 
differently  coloured  rays  is  observed,  the  white  light  being 
resolved  into  its  various  coloured  constituents.  The  coloured 
band  thus  obtained  is  called  a  spectrum,  and  white  light  gives 
a  continuous  spectrum,  stretching  from  red  (which  is  the  least 
refrangible)  to  violet  (the  most  refrangible).  If,  now,  the 
light  from  a  coloured  flame  be  allowed  to  fall  through  a 
narrow  slit  on  to  the  prism,  we  get  a  spectrum  which  consists 
only  of  a  few  bright-coloured  bands.  Thus  the  yellow  sodium 
flame,  when  treated  in  this  way,  gives  two  bright  yellow  lines 
close  together,  while  the  violet  flame  of  potassium  gives  two 
bright  lines,  one  in  extreme  red  and  the  other  in  extreme 
violet.  These  peculiar  lines,  or  sets  of  lines,  are  absolutely 
characteristic  of  the  chemical  element  in  question,  and  are 

62 


THE  SPECTROSCOPE  63 

exhibited  by  no  other  substance ;  further,  the  position  of  each 
line  in  the  spectrum  is  definitely  fixed,  and  never  alters  for 
any  given  apparatus.  Hence,  suppose  we  examine  the  flame 
given  by  a  mixture  of  sodium  and  potassium  salt,  we  see  the 
red  and  purple  lines  in  their  respective  portions  of  the  spec- 
trum, and  the  yellow  sodium  lines  in  between,  just  as 
distinctly  as  when  only  one  element  is  there  alone.  Some 
elements  give  a  great  many  coloured  bands,  but  no  matter, 
the  same  element  will  always  give  exactly  the  same  number 
of  bands,  in  precisely  the  same  position,  no  matter  what 
the  source  of  the  element  originally  may  be.  If  a  number 
of  elements  are  present,  then  the  spectrum  is  made  up 
of  the  spectrum  of  each  separate  element,  and  in  most  cases 
the  spectrum  can  be  analyzed  into  groups,  and  the  elements  in 
this  way  identified  ;  in  other  words,  an  analysis  of  the  mixture 
can  be  made. 

A  great  advantage  of  this  method  of  analysis  is  its  extreme 
delicacy,  as  well  as  in  the  great  facility  with  which  the  pres- 
ence of  particular  elements  can  be  detected  with  certainty. 
Thus  the  y^^.^o.^o^  °f  a  sodium  salt  can  be  detected  ;  lithium 
to  the  extent  of  1  part  in  6,000,000.  In  this  way  the  presence 
of  substances  can  be  made  manifest  where  hitherto  they  have 
eluded  detection.  For  example,  lithium,  which  was  formerly 
supposed  to  exist  only  in  four  minerals,  has  been  detected  in 
almost  all  spring  waters,  in  tea,  tobacco,  milk,  and  blood. 

Again,  certain  samples  of  sodium  and  potassium  exhibited 
certain  lines  which  were  entirely  absent  in  other  samples,  yet 
the  additional  lines  did  not  belong  to  any  then  known  sub- 
stance. What  was  the  result  of  this  observation  1  The  dis- 
covery of  the  alkali  metals,  rubidium  and  caesium,  in  1860 
by  Bunsen.  These  metals  had  previously  eluded  detection 
simply  because  they  occurred  in  such  minute  quantities  that  it 
was  absolutely  impossible  to  detect  them  by  ordinary  ana- 
lytical methods.  Since  Bun  sen's  discovery  of  rubidium  and 
cgesium  the  spectroscope  has  been  the  means  of  revealing 
quite  a  number  of  previously  unknown  elements. 

It  is  not  only  those  bodies  which  have  the  power  to  impart 
colour  to  a  flame  which  yield  characteristic  spectra,  this 
property  belongs  to  every  elementary  substance,  whether 
metal,  non-metal,  solid,  liquid,  or  gas ;  and  it  is  always 
observed  when  such  an  element  is  heated  to  the  point  at 
which  its  vapour  becomes  luminous,  for  at  this  point  each 


64 


SPECTRUM  ANALYSIS 


element  emits  its  own  specific  light,  and  the  characteristic 
bright  lines  are  apparent  on  observing  the  spectrum. 

The  majority  of  the  metals  require  a  much  higher  tempera- 
ture than  the  ordinary  flame  in  order  to  make  their  vapours 
luminous ;  they  may,  however,  be  easily  heated  up  to  the 
required  temperature  by  means  of  an  electric  spark,  which 
volatilizes  a  little  of  the  metal  in  passing  between  two  points, 
and  heats  it  to  an  intensity  sufficient  to  enable  it  to  emit  its 
own  peculiar  light.  Thus,  all  metals  (including  iron,  platinum, 
gold,  silver,  etc.)  can  be  recognized  by  means  of  their 
spectra. 


FIG.  38 

The  permanent  gases,  such  as  hydrogen,  can  be  rendered 
luminous  by  means  of  an  electric  spark,  and  their  spectra 
mapped  out.  Thus  the  red  light  of  the  incandescent  hydrogen 
is  resolved  into  one  bright  red,  one  blue,  and  two  violet 
lines.  There  are  two  distinct  types  of  spectra — namely,  line 
spectrum,  which  is  made  up  of  a  number  of  sharply  defined 
coloured  lines  (really  images  of  the  slit),  and  band  spectrum, 
which  consists  of  bands  which  are  broad,  even  with  a  very 
narrow  slit.  These  bands  are  often  sharp  on  one  side,  and 
gradually  fade  away  on  the  other. 

The  Spectroscope — This  instrument  is  somewhat  as  shown 
in  Fig.  38.  It  consists  of  a  prism,  A,  which  is  firmly  fixed  on 
an  iron  base  ;  a  collimator,  B,  which  carries  an  adjustable  slit 
at  one  end  and  a  lens  at  the  other  end,  by  means  of  which  the 


THE  SPECTROSCOPE  66 

light  from  the  coloured  flame  E  is  rendered  parallel  before 
falling  on  the  prism  A.  The  light,  having  been  refracted  by 
the  prism,  is  received  by  the  telescope  F,  and  the  image  magni- 
fied before  reaching  the  eye.  In  many  instruments  the  slit  is 
half  covered  with  a  small  prism.  By  this  means  it  is  possible 
to  obtain  two  spectrum  bands  at  the  same  time  from  two 
different  flames.  One  is  arranged  so  that  the  rays  pass 
directly  through  the  uncovered  portion  of  the  slit.  The  rays 
from  the  second  flame  first  strike  the  small  prism,  and  are  then 
reflected  through  the  slit  and  along  the  collimator  on  to  the 
prism.  Usually  one  flame  gives  a  standard  spectrum,  which 
helps  to  emphasize  any  special  characteristics  of  the  substance 
tested.  The  tube  G  contains  a  scale  which  is  illuminated  by 
the  white  light  from  H.  This  scale  is  distinctly  visible  in  the 
telescope,  and  by  it  the  position  of  any  coloured  spectrum 
line  can  be  definitely  fixed. 

Adjustment  of  the  Spectroscope. — It  has  already  been  pointed 
out  that  the  rays  of  light  leaving  the  collimator  should  be 


parallel.  This  is  achieved  by  adjusting  the  distance  between 
the  slit  and  the  collimator  lens.  First  bring  the  spectroscope 
near  a  window,  and  observe  through  the  telescope  some 
distant  object ;  focus  the  telescope  by  means  of  the  adjusting 
screw  until  that  object  is  seen  clearly.  The  telescope  is  then 
focussed  for  parallel  light.  Now  bring  the  telescope  into  the 
dark-room,  and  illuminate  the  slit  of  the  collimator  by  means 
of  a  sodium  flame ;  then  adjust  the  collimator  by  sliding  it  in 
or  out  until  the  image  of  the  slit  is  seen  quite  sharply.  Now 
illuminate  the  scale,  and  adjust  it  so  that  the  sodium  line  is 
about  a  third  the  distance  from  the  left-hand  side  of  the  scale. 
Remember  it  is  necessary  to  have  the  spectra  as  bright  as 
possible.  This  depends  upon  the  position  of  the  sodium  flame 
relative  to  the  slit.  The  importance  in  securing  the  correct 
position  of  the  flame  will  be  better  understood  from  Fig.  39. 
Let  A,  Bj  C,  D  represent  a  section  of  the  collimator,  B^  D  the 
lens,  and  S  the  slit,  also  &,  E"^  E™ — three  different  positions 
5 


66  SPECTRUM  ANALYSIS 

of  the  flame.  At  position  E'  only  part  of  the  flame  is  used  to 
illuminate  the  collimator  ;  at  position  E'ff  the  outside  portions 
of  the  lens  are  not  illuminated  at  all.  It  is  only  at  the  position 
E"  that  the  lens  is  illuminated  with  the  maximum  amount  of 
light.  This  position  must  in  all  eases  be  determined  by  trial. 

Mapping  oj  Spectra — Prepare  several  pieces  of  platinum 
wire  (thickness  1  mm.)  sealed  into  glass  tubes.  Clean  them 
thoroughly  by  moistening  with  pure  concentrated  hydro- 
chloric acid  and  heating  white  heat  in  bunsen.  Repeat  this 
process  until  the  wire  imparts  no  coloration  to  the  bunsen 
flame.  The  student  should  also  provide  himself  with  a  sheet 
of  paper  on  which  are  ruled  lines  divided  into  millimetre 
divisions.  Now  take  one  of  the  wires  and  moisten  it  with 
pure  concentrated  hydrochloric  acid,  dip  the  wire  into  a  little 
solid  sodium  chloride,  causing  a  little  to  adhere  to  the  wire. 
Now  place  the  wire  in  the  hottest  part  of  the  flame — i.e.,  just 
above  the  cone  (this  portion  of  the  flame  should  be  adjusted 
so  as  to  be  opposite  to  the  slit) — and  observe  the  position  of 
the  sodium  line  on  the  scale.  Mark  the  position  on  one  of  the 
lines  on  your  scale-paper,  each  division  on  your  scale  corre- 
sponding, say,  to  1  mm.  on  your  paper.  On  a  second  wire, 
moistened  with  hydrochloric  acid,  place  a  small  quantity 
of  barium  chloride,  and  in  a  similar  manner  map  out  the 
spectrum.  One,  and  perhaps  two,  bright  green  lines  should 
be  visible  in  this  case  ;  if  this  is  not  so,  the  slit  requires 
adjusting.  Repeat  this  with  fresh  platinum  wires  with  the 
chlorides  of  lithium,  thallium,  strontium,  calcium,  and  potas- 
sium. In  the  case  of  potassium  there  is  a  very  distinct 
red  line  and  also  a  line  in  the  violet,  but  this  is  often 
very  difficult  to  see,  except  by  experienced  observers.  The 
violet  can  usually  be  seen  by  removing  the  light  which 
illuminates  the  scale  and  readjustment  of  the  slit ;  then, 
having  noted  its  approximate  position,  it  can  often  be  detected 
on  illuminating  the  scale  again,  and  hence  its  position 
obtained. 

In  the  case  of  calcium  and  other  salts  it  will  be  observed 
that  the  spectrum  changes.  The  first  spectrum  is  due  to  the 
chloride,  which  is  gradually  replaced  by  that  of  the  oxide. 

The  spectrum  of  an  incandescent  solid  is  continuous  ;  a  dis- 
continuous spectrum  of  bright  lines  is  only  produced  by  an 
incandescent  gas.  The  yellow  line  seen  when  a  salt  of  sodium 
is  heated  on  a  platinum  wire  in  the  bunsen  flame  is  due  to  the 


THE  SPECTROSCOPE 


67 


vapour  of  sodium  set  free  by  the  temperature  of  the  flame,  or 
by  chemical  change  taking  place  between  the  substance  and 
the  hot  gases  of  the  flame.  The  carbonates,  chlorides,  or 
nitrates  of  the  alkaline  earths  are  convenient  to  use,  but  the 
chlorates,  where  possible,  are  preferable,  since  as  a  consequence 
of  the  liberation  of  oxygen  the  flame  is  hotter. 

The  actual  number  of  lines  visible  depends  upon  the  tem- 
perature of  the  flame.  Thus  a  flame  of  hydrogen  burning  in 
chlorine  does  not  give  the  sodium  line  when  sodium  is  intro- 


20    30     4O     5O     60     70    00     90    WO    HO    120    130   OO  ISO   160 


10    JO     4-0    50    60     70    80     90    100    I/O    120    130   140    ISO    160 


H 


20   3O   40   50   60  7O    QO  90   100  HO  120  130  140  ISO  160 
FIG.  40 

duced  into  it ;  or,  again,  the  sodium  line  is  hardly  visible  in  a 
flame  of  sulphuretted  hydrogen  burning  in  air.  If,  on  the 
other  hand,  much  hotter  flames  are  used,  such  as  the  oxy- 
hydrogen  flame,  then  new  lines  are  revealed.  Thus,  with  such 
a  flame  sodium  gives  five  lines  at  43'2,  5OO,  56'0,  76'0,  83-6, 
whereas  in  the  electric  spark  spectra  of  sodium  eight  lines  are 
visible. 

Bunsen  flame  spectra  are  somewhat  as  follows  (Fig.  40) : 


68  SPECTRUM  ANALYSIS 

Sodium — A  bright  yellow  line  at  position  50*0.  This  line  is 
a  standard,  and  is  known  as  the  D  line. 

Lithium  salts  colour  the  flame  crimson.  The  spectrum  con- 
sists of  two  lines,  a  very  brilliant  one  at  31'7,  and  a  much 
feebler  line  at  45-0.  The  red  line  should  be  quite  distinct. 

Potassium  gives  one  line  in  the  extreme  red  at  17 '5,  and 
another  in  the  extreme  violet  at  153-0. 

Alkaline  Earths — The  spectra  of  the  alkaline  earths  are  not 
so  simple  as  those  of  the  alkalies.     When  first  introduced 
into  the  flame  there  are  seen  certain  bands  which  are 
"X      different  according  to  the  particular  salt  of  the  metal 
>^>     used,  and  which  are  supposed  to  be  due  to  the  com- 
pound employed,  but  the  final  spectrum  is  the  same 
with  all  salts,    which  is   partly   due   to    the    oxide, 
besides  which   the  brightest  lines  of   the  metal  are 
also  visible. 

Calcium  is  recognized  by  its  characteristic  orange 
band,  40-0-43-0,  and  the  green  band,  61-0-63-0. 
Chloride,  chlorate,  bromide,  give  the  best  results. 
Non-volatile  salts  should  be  treated  with  hydro- 
chloric acid  if  it  decomposes  them,  or  heated  with 
ammonium  fluoride. 

Strontium  gives  an  orange  band  at  44fO-47'0,  red 
lines  30-0-35-0,  but  the  most  characteristic  is  the  blue 
line  at  107 -6.  The  best  salts  to  use  are  chloride  or 
chlorate ;  the  lines  are  not  visible  with  silica,  silicate, 
phosphate,  etc. 

Barium  gives  brilliant  green  bands  at  73-0  and  78-0. 

\\J        Hydrogen  Spectrum — In  the  case  of  hydrogen,  the 
iir     spectrum  is  obtained  by  using  exhausted  tubes,  such 
fc       as  Geissler  or  Plucker  tubes.     Such  a  tube  is  shown 
FIG.  41  jn  -ffig.  41 1     The  electrodes  of    platinum  are  sealed 
into  the  glass,  one  at  each  end  of  the  tube,  and  the 
central  portion  is  a  capillary  tube.     It  is  the  capillary  portion 
which  is  placed  in  front  of  the  slit  of  the  spectroscope,  while 
a  discharge  is  passed  through  the  tube  by  means  of  an  induc- 
tion coil.     If  the  tube  contains   "  rarefied "  hydrogen,  then 
the   discharge   is    red,   which,    when   observed  through  the 
spectroscope,  shows  the  red  (C  line)  at  34-0,  blue  (F  line)  at 
92-0,  and  two  violet  (£'  G"  lines)  at  127-5  and  151-0  respec- 
tively.    The  red  and  blue  are  the  most  conspicuous. 


REDUCTION  OF  SPECTROSCOPIC  MEASUREMENTS    69 


The  student  should  obtain  such  a  tube  and  map  out  the 
spectrum  as  before. 

Reduction  of  Spectroscopic  Measurements  to  an  Absolute 
Scale — When  the  spectrum  of  a  given  substance  is  mapped,  the 
relative  positions  of  the  lines  will  be  found  to  differ  according 
to  the  instrument  used.  Even  if  the  sodium  line  is  at  the 
same  scale  division  in  each,  the  readings  of  the  other  lines  will 
differ  in  the  different  instruments,  since  they  depend  upon  the 
dispersion  of  the  prism  and  on  the  distance  between  the 
divisions  of  the  scale.  The  student  must  not,  therefore, 
expect  his  readings  to  coincide  with  the  scale  number  here 
given  as  examples,  as  this,  except  by  mere  coincidence,  will 
not  be  the  case.  The  numbers  and  positions  of  the  lines  on 
the  diagrams  are  for  one  particular  prism  and  for  one  particular 
scale.  The  student  will  therefore  at  once  see  the  importance 
of  being  able  to  standardize  his  readings  so  that  they  may  be 
comparable  with  the  readings  obtained  on  any  other  instru- 
ment. In  other  words,  the  student  must  be  able  to  represent 
his  results  in  a  manner  which  is  entirely  independent  of  his 
instrument.  This  is  done  by  reducing  the  measurements 
taken  on  the  arbitrary  scale  to  wave  lengths.  There  are 
several  methods  by  which  this  may  be  done,  but  only  one  need 
be  considered  here — namely,  what  is  known  as  the  graphical 
interpolation  method.  In  this  method  the  positions  of  three  (or 
more)  lines,  the  wave  lengths  of  which  are  known,  are  observed 
on  the  arbitrary  scale  of  the  spectroscope,  and  the  unknown 
wave  lengths  of  other  lines  are  obtained  by  interpolation. 

For  our  purpose  we  will  take  six  standard  lines  of  known 
wave  length,  whose  position  on  the  scale  of  a  certain  instru- 
ment are  as  quoted — viz. : 


The  Chloride  of  — 

Line  taken 

Wave  Length 

Scale  Reading 

Potassium 

Red 

7669 

17'5 

Lithium  ... 

Red 

6708                 31-7 

Strontium 

Orange 

6409                 40'0 

Sodium  ... 

Yellow 

5893                 50-0 

Thallium 

Green 

5351 

69-0 

Strontium 

Violet 

4608               107-6 

The  wave  lengths  are  given  in  Angstrom  units,  where  1  unit 
mm<  (0*1  w)'    Having  noted  the  position  of  the 


70 


SPECTRUM  ANALYSIS 


above  six  lines  on  the  scale,  and  given  their  wave  lengths,  it 
is  only  necessary  now  to  draw  a  curve,  the  scale  readings  taken 
as  the  abscissae,  and  the  corresponding  wave  lengths  as  ordi- 
nates  (see  Fig.  42) ;  connect  the  separate  points  by  a  smooth 
curve,  1  mm.  representing  one  division  on  the  scale,  and,  say, 
1  mm.  on  the  ordinate  representing  40  wave-length  units. 
From  this  curve  the  wave  length  may  be  read  that  corresponds 
to  each  division  on  the  scale. 


10  20    JO    40  50    60   70  80   90    100  HO    120  /30  140 

Scale  Reading. 
FIG.  42 

Exercise :  Determine  the  Wave  Lengths  of — 

(a)  Hydrogen  (C  and  F  lines). 

(b)  Barium  (green  lines). 

(c)  Calcium  (orange  lines). 

The  student  should  now  try  one  or  two  "  unknowns," 
selected  from  those  whose  spectrum  he  has  already  mapped, 
by  first  mapping  the  spectrum  of  the  unknown,  and  then,  by 
comparison  with  the  spectra  previously  prepared,  determine 
what  the  metal  is. 

If  time  permits,  he  should  map  the  spectrum  of  a  mixture  of 
two  or  three  metals. 


CHAPTER  XI 
DETERMINATION  OF  PARTITION  COEFFICIENTS 

Distribution  of  a  Substance  between  Two  Non-Miscible 
Solvents — When  succinic  acid  is  shaken  up  with  two  immis- 
cible liquids,  such  as  ether  and  water,  the  distribution  which 
takes  place  is  very  similar  to  the  distribution  of  a  substance 
between  a  liquid  and  a  gas  phase  (solution  of  a  gas  in  a  liquid), 
and  therefore  similar  rules  apply  to  the  distribution  of  a  sub- 
stance between  two  immiscible  solvents  as  to  the  solution  of 
gases.  These  may  be  expressed  as  follows  : 

1.  If  the  molecular  weight  of  the  solute  is  the  same  in  both 
solvents,  the  distribution  coefficient  (i.e.,  the  ratio  in  which 
the  solute  distributes  itself  between  the  two  solvents)  is  constant 
at  constant  temperature  (Henry's  law). 

2.  In  the  presence  of  several  solutes  the  distribution  of 
each  solute  separately  takes  place  as  if  the  others  were  entirely 
absent.     (This  corresponds  to  Dalton's  law  of  partial  pres- 
sure.) 

3.  The  ratio  in  which  the  solute  is  distributed  between  two 
solvents  depends,  however,  not  only  on  its  solubility  in  each 
solvent,  but  also   on   whether  it  possesses  the  same  molar 
weight  in  the  two  solvents.     Hence  a  study  of  these  relation- 
ships is  of  vital  importance,  in  so  far  as  they  afford  a  means 
of  determining  the  state  of  association  or  dissociation  of  a  sub- 
stance in  solution. 

This  will  be  better  understood  from  a  consideration  of  the 
following  results  given  by  Nernst : 

Distribution  of  Succinic  Acid  between  Ether  and  Water  — 
Varying  quantities  of  succinic  acid  were  shaken  up  with 
water  and  ether  and  the  distribution  coefficient  determined 
where  CT  is  the  concentration  in  water  and  C2  the  concentra- 

71 


72      DETERMINATION  OF  PARTITION  COEFFICIENTS 


tion  in  ether.     The  approximate  constancy  of  this  ratio  shows 
that  Henry's  law  applies. 


Ci  (Water) 

C2  (Ether) 

Si 

Co 

0024 

0-0046 

5-2 

0-070 

0-013           5'2 

0-121 

0-022 

5-4 

When,  however,  benzoic  acid  is  shaken  up  with  benzene  and 
water •,  Nernst  gives  the  following  results  : 


Ci  (Water 

C2  (Benzene) 

C2 

Ci 

0-0150 
0-0195 
0-0289 

0-242 
0-412 
0-970 

0-062 
0-048 
0-030 

0-0305 
0-0304 
00293 

It  will  be  observed  that  in  this  the  ratio  *r  is  not  constant, 


*r  i 


but  the  ratio     JL  is  constant. 

V     2 

These  results  show  that  while  benzoic  acid  has  a  normal 
molecular  weight  in  water,  it  consists  almost  entirely  of  double 
molecules  in  benzene.  In  such  a  case  the  concentration  of 
the  single  molecules  in  benzene  is  proportional  to  square  root 
of  the  total  concentration.  Since  a  constant  ratio  should  be 
found  between  the  concentration  of  the  single  molecules  in 
the  first  solvent  and  the  single  molecules  of  the  second  solvent, 

it  follows  that  — =  must  be  a  constant  (Law  of  Mass  Action, 


Dilution  Law,  etc.). 

Generally  this  law  may  be  stated,  that  if  in  one  solvent  the 
solute  is  present  as  simple  molecules,  and  in  the  second 
solvent  in  "  n  "  simple  molecules  are  associated  as 


PARTITION  COEFFICIENTS  73 

and  Ct  is  the  concentration  in  the  first  solvent  and  C2  in  the 
pi 

second,  then  the  ratio      JL  should  be  a  constant. 

V     2 

Experiment  to  Determine  the  Distribution  Coefficient  of  Succinic 
Acid  between  Ether  and  Water — Take  a  well- stoppered  bottle,  and 
introduce  100  c.c.  of  distilled  water  (free  from  CO2)  in  which 
1  gram  of  succinic  acid  has  been  dissolved.  Add  an  equal 
volume  of  ether.  Fix  the  stopper  securely,  and  immerse  the 
bottle  up  to  the  neck  in  a  thermostat  at  25°  C.  Shake  the 
bottle  vigorously  every  five  minutes  for  about  forty  minutes. 
Determine  the  concentration  of  acid  in  each  layer  by  carefully 
removing  25  c.c.  of  solution  with  a  pipette.  The  titration 

should  be  done  with-^  baryta  solution,  using  phenolphthalein 

as  an  indicator. 

Repeat  the  experiment,  using  2  per  cent,  and  5  per  cent, 
solutions  respectively,  and  determine  in  each  case  the  value  of 

r\ 

the  ratio  ?y . 

Experiment  to  Determine  the  Distribution  Coefficient  of  Benzoic 
Acid  between  Water  and  Benzene — Prepare  three  solutions  of 
benzoic  acid  in  benzene  containing  12,  6,  and  3  per  cent  of 
benzoic  acid  respectively.  To  100  c.c.  of  benzene  solution 
add  100  c.c.  of  distilled  water,  and  proceed  exactly  as  in  the 
previous  experiment.  Since  at  the  concentrations  used  in 
these  experiments  benzoic  acid  exists  mainly  as  (C6H6COOH)2 
— i,e.,  associated  molecules  in  the  benzene  solution — the  ratio 

-£=  should  be  constant. 

V^2 

Experiment  to  Find  the  Degree  of  Association  of  Benzoic  Acid 
in  Chloroform — Repeat  exactly  the  previous  experiment,  using 

chloroform  instead  of  benzene,  and  find  what  value  of  n  in  the 
p 

ratio      _  gives  a  constant.     This  value  is  the  number  of 
molecules  which  are  associated  in  the  chloroform  solution. 


CHAPTER  XII 
THERMO-CHEMICAL  MEASUREMENTS 

Hess's  Law — When  the  same  chemical  change  takes  place 
between  two  definite  amounts  of  two  substances  under  the  same 
conditions,  the  same  amount  of  heat  is  always  given  out,  pro- 
vided that  the  final  products  or  product  are  the  same  in  each 
case. 

The  actual  heat  effect,  absorbed  or  evolved,  depends  on  (a) 
the  nature  of  the  reaction,  (6)  the  physical  conditions  of  the 
reacting  substances,  and  (c)  the  amounts  of  the  substances 
present.  Usually  the  heat  of  a  reaction  is  measured  by  the 
method  of  mixtures. 

The  value  of  the  thermal  effect  measured  in  calories  (cal.) 
is  usually  too  large,  and  the  last  figure  uncertain,  so  a  larger 
unit  is  used,  equal  to  100  cals.  This  larger  caloric  is  usually 
represented  by  K,  and  is  practically  equal  to  the  amount  of 
heat  required  to  raise  1  gram  of  water  from  0°  to  100°.  A 
larger  caloric  still,  due  to  Berthelot,  is  now  considerably  used, 
and  is  equal  to  1000  calories,  and  is  represented  by  Cal.,  as 
distinguished  from  cal. 

Heat  of  Neutralization — By  the  heat  of  neutralization  of 
a  monobasic  acid  and  a  base  is  meant  the  amount  of  heat 
given  out  when  1  gram  molecule  of  acid  and  1  gram 
molecule  of  the  base,  dissolved  in  water,  are  mixed. 

For  polybasic  acids,  as  many  heats  of  neutralization  are 
possible,  as  there  are  basicities  for  each  acid. 

The  reaction  is  caused  to  take  place  in  a  calorimeter,  which 
should  be  preferably  of  platinum  or  silver,  but  nickel,  copper, 
or  aluminium  may  be  used.  It  should  have  a  capacity  of 
about  600  c.c.  The  outer  surface  of  this  calorimeter  should 
be  polished.  This  is  then  surrounded  by  at  least  two  other 
vessels,  polished  on  the  inside,  and,  if  possible,  a  water-jacketed 

74 


HEAT  OF  NEUTRALIZATION 


75 


vessel  should  surround  these.  In  each  case  the  respective 
calorimeters  are  insulated  from  one  another  by  wooden  blocks. 
The  two  inner  vessels  should  be  fitted  with  non-conducting 
lids,  with  two  holes  in  each,  to  admit  a  stirrer  (glass)  and  a 
thermometer,  reading  at  least  in  tenths(better  use  a  Beckmann). 
Experiment  to  Determine  the  Heat  Neutralization  of  Hydro- 
chloric Acid  by  Caustic  Soda  —  Prepare  250  c.c.  of  a  semi- 
normal  solution  of  caustic  soda  and  hydrochloric  acid,  and 
determine  accurately  the  strength.  The  caustic  soda  should 


\ 


V//////////////////////A 

FIG.  43 


be  free  from  carbonate.  Fit  up  the  apparatus  as  shown  in 
Fig.  43,  and  measure  out  into  the  inner  calorimeter  250  c.c. 
of  caustic  soda. 

Into  a  flask  (previously  washed  out  with  i>  HC1),  protected 
with  at  least  two  polished  metal  cylinders,  to  reduce  loss 
by  radiation,  introduce  250  c.c.  of  hydrochloric  acid.  A 
sensitive  thermometer  (graduated  at  least  in  tenths)  is  sup- 
ported in  the  hydrochloric  acid.  This  thermometer  must 
have  been  previously  compared  with  that  in  the  alkali.  In 
order  to  allow  for  the  loss  of  heat  by  radiation,  it  is  necessary 
to  determine  the  rate  of  change  of  temperature  of  both  acid 


76 


THERMO-CHEMICAL  MEASUREMENTS 


and  alkali  before  mixing,  and  then  of  the  mixture  by  taking 
readings,  say  every  minute,  for  about  seven  minutes  before 
the  solutions  are  mixed,  then  mix  the  solutions  quickly,  con- 
stantly stirring,  and  again  take  readings  for  a  similar  period. 
(Note — /j  should  be  as  near  as  possible  equal  to  t2.) 

In  order  to  determine  the  true  temperature  which  should 
have  resulted,  it  is  necessary  to  plot  the  above  readings.  This 
is  illustrated  in  Fig.  44. 

The  curves  ^  and  t2  give  the  temperatures  for  alkali  and 
acid  respectively.  After  seven  minutes,  the  solutions  are 


2      3 


456 

Time 


89      W    II     12     13     14- 


FIG.  44 

mixed,  then  the  temperature  continues  to  rise,  rapidly  at  first, 
for  about  three  minutes,  after  which  it  falls  gradually. 

The  bend  in  the  curve  is  obviously  due  to  loss  by  radiation 
whilst  the  mixture  was  becoming  heated,  since  a  time-cooling 
curve  would  be  straight.  The  direction  of  the  true  curve  is, 
however,  given  by  the  last  few  readings.  Hence,  by  extra- 
polation, the  true  elevation  temperature,  ty  can  be  found  by 
drawing  a  perpendicular  at  the  point  which  indicates  the 
instant  of  mixing  (seventh  minute),  and  reading  off  the  tem- 
perature at  the  point  where  this  line  cuts  the  extrapolated 


HEAT  OF  NEUTRALIZATION  77 

cooling  curve  —  i.e.,  the  temperature  reading  thus  obtained  is 
used  in  calculating  the  result. 

Calculation  —  The  heat  evolved  is  represented  by  the  follow- 
ing equation  — 


~^)  J, 


where  mv  m^,  ra3,  mv  are  the  masses  of  the  solution,  calori- 
meter, thermometer,  and  stirrer  respectively,  and  a,  ft,  y,  8, 
their  respective  specific  heats. 

As  regards  the  solution,  it  will  be  sufficiently  accurate  in 
this  case  to  take  the  water  equivalent  of  the  solution  as  equal 
to  the  mass  of  water  contained  in  it  —  i.e.,  equal  to  the  volume 
of  the  solution  approximately.  In  the  case  of  the  thermo- 
meter we  do  not  know  the  relative  weights  of  the  glass  and 
mercury,  but  we  may  make  use  of  the  fact  that,  volume  for 
volume,  the  specific  heats  of  glass  and  mercury  are  practically 
identical,  and  equal  to  0*47  per  c.c. 

To  find  the  volume  of  the  thermometer  immersed  in  the 
solution  insert  it  in  a  burette,  partially  filled  with  water,  up 
to  the  depth  it  is  immersed  in  the  solution,  and  measure  the 
displacement.  If  the  thermometer  is  not  solid,  as  in  the  case 
of  a  Beckmann,  the  volume  of  the  bulk  and  the  requisite 
portion  of  the  stem  must  be  found  separately,  and  the  volume 
found  for  the  stem  divided  by  five,  and  this  value  added  to 
the  volume  for  the  bulb. 

In  place  of  the  ordinary  calorimeter  a  Dewar  vacuum  vessel 
may  be  conveniently  substituted,  to  reduce  the  loss  of  heat. 
Repeat  the  above  experiments,  using  ammonium  hydroxide  and 
sulphuric  acid,  also  caustic  potash  and  acetic  acid. 

In  accordance  with  the  theory  of  electrolytic  dissociation,  the 
heat  of  neutralization  of  any  completely  dissociated  base  is 
constant,  since  the  reaction  consists  solely  of  the  union  of  H* 
and  OH'  ions  giving  unionized  water.  In  the  ease  of  hydro- 
chloric acid  and  caustic  soda  it  may  be  represented  thus  — 

H-  +  Cl'  +  Na-  +  OH'  =  Na-  +  Cl'  +  H20. 

The  value  of  this  constant  is  13*7. 

When  it  is  required  to  determine  the  heat  of  neutralization 
of  a  polybasic  acid  with  a  monovalent  base,  or  vice  versa,  the 
thermal  effect  must  be  calculated  for  each  basicity  separately. 

In  case  precipitates  are  formed,  the  heat  of  precipitation 


78  THERMO-CHEMICAL  MEASUREMENTS 

must  be  subtracted  from  the  heat  evolved  (see  later  section). 
If  the  acid  or  base  is  a  solid  or  gas,  a  correction  for  heat  of 
fusion-solution,  or  absorption  must  be  applied  when  possible. 
For  example,  when  caustic  soda  solution  is  neutralized  by 
gaseous  CO2,  we  get  a  certain  heat  effect,  2NaOHAq  +  C02; 
but  to  get  the  true  heat  of  neutralization  the  heat  of  absorp- 
tion of  C02  must  be  subtracted — i.e.,  C02Aq. 

.-.  2NaOHAq.C02  -  C02Aq.  =  2NaOHAq.CO2Aq. 

Heat  of  Solution — The  heat  of  solution  of  a  substance  is  the 
thermal  effect  produced  by  dissolving  1  gram  molecule  of 
a  substance  in  a  given  number  of  molecules  of  solvent. 

The  heat  of  solution  may  be  sometimes  positive  and  some- 
times negative,  that  is,  heat  may  be  evolved  or  absorbed. 

It  varies  with  the  quantity  of  solvent  used.  If  further 
dilution  produces  no  further  heat  effect,  the  heat  measured 
for  1  gram  molecule  is  known  as  the  heat  of  solution  at  infinite 
dilution. 

Experiment  to  Determine  the  Heat  of  Solution  of  Sodium  Chloride 
— The  method  is  similar  to  that  employed  for  heat  of  neutral- 
ization. Into  the  calorimeter  introduce  500  grams  of  water, 
and  fit  up  the  apparatus  with  thermometer  and  stirrer  as 
before,  taking  the  same  precautions  as  to  temperature  read- 
ings. Weigh  out  into  a  dry  test-tube  10  grams  of  finely 
powdered  dry  sodium  chloride.  Place  the  test-tube  in  a  beaker 
filled  with  water  at  a  known  temperature  (which  should,  as 
near  as  possible,  be  at  the  same  temperature  as  the  water  pre- 
viously weighed  out).  When  the  salt  has  acquired  the  tem- 
perature of  the  bath,  remove  the  test-tube,  dry  it  roughly, 
and  empty  the  contents  into  the  calorimeter  and  stir  rapidly, 
and  take  readings  every  minute  for  seven  or  eight  minutes. 

Plot  the  temperature  readings  against  time,  and  eventually 
determine  the  maximum  elevation. 

The  method  of  calculation  is  similar  to  the  previous  experi- 
ment. Consider  the  solution  as  pure  water  for  calculation. 

Repeat  the  above  experiment  with  MgSO47H2O  and 
ZnS047H20. 

Heat  of  Hydration — The  heat  of  hydration  is  the  quantity 
of  heat  liberated  when  1  gram  molecule  of  substance  combines 
with  a  definite  number  of  molecules  of  water  to  form  a 
hydrate. 


HEAT  OF  DILUTION  79 

The  heat  of  hydration  is  obtained  by  determining  the  heat 
of  solution  of  the  hydrated  and  anhydrous  forms  of  the  salt, 
and  subtracting  the  latter  from  the  former. 

The  method  of  experiment  is  therefore  essentially  that  for 
determining  the  heat  of  neutralization  and  solution. 

Experiment  to  Determine  the  Heat  of  Hydration  of  Copper 
Sulphate — 

(a)  Determine  the  heat  of  solution  of  GuS045H20. 

(b)  Determine  the  heat  of  solution  of  CuS04. 

Then  (b  -  a)  =  heat  of  hydration. 

Heat  of  Dilution — By  heat  of  dilution  is  meant  the  quantity 
of  heat  liberated  or  absorbed  when  a  solution  is  further  diluted 
by  the  solvent. 

The  method  here  again  is  similar  to  the  determination  of 
heats  of  neutralization.  The  result  is  expressed  as  the  amount 
of  heat  change  resulting  from  a  given  increase  of  solvent. 
Both  the  initial  and  final  concentrations  must  be  stated  in 
the  result.  It  is  equal  to  the  difference  between  the  heats 
of  solution  for  the  two  respective  volumes  of  solvent. 

Experiment  to  Determine  the  Heats  of  Dilution  of  a  3  per 
Cent.  Solution  of  Potassium  Nitrate — Dissolve  12  grams  of  nitrate 
in  400  grams  of  water,  and  determine  the  heat  evolved  on 
adding  100  grams  of  water. 

Heat  of  Precipitation — The  heat  of  precipitation  is  the 
quantity  of  heat  evolved  when  a  gram  molecule  of  substance 
separates  out  from  a  solution. 

It  is  the  converse  of  heat  of  solution,  and  is  numerically 
equal  to  it. 

Experiment  to  Determine  the  Heat  of  Precipitation  of  Silver 
Chloride — Dissolve  1  gram  of  sodium  chloride  in  500  c.c.  of 
water,  and  place  it  in  a  calorimeter  fitted  up  as  before.  Prepare 
15  c.c.  of  normal  silver  nitrate  at  the  same  temperature. 
When  the  temperatures  are  equal,  mix  the  solutions,  and  note 
the  change  in  temperature.  From  the  results  calculate  the 
heat  of  precipitation.  Details  of  the  experiment  are  the  same 
as  in  the  previous  cases. 

The  result  is  the  same  as  the  heat  of  solution  with  the 
opposite  sign. 

Heat  of  Combustion — The  heat  of  combustion  of  a  substance 
is  the  quantity  of  heat  evolved  in  the  complete  combustion 
of  1  gram  molecule  of  substance. 


80 


THERMO-CHEMJCAL  MEASUREMENTS 


Let  x  be  the  amount  of  substance  used  in  the  experiment, 
and  M  the  molecular  weight  of  the  substance  ;  also  let  W  be 
^  the  weight  of  water  in  the 

calorimeter,  and  w  the  water 
equivalent  of  the  appara- 
tus, Tx  and  T2  the  initial 
and  final  temperature,  then 
Q,  the  heat  of  combustion, 
will  be  given  by — 


The  reaction  is  usually 
caused  to  take  place  in  com- 
pressed oxygen  inside  a 
calorimetric  bomb. 

A  convenient  form  of 
bomb  is  as  shown  in  Fig.  45. 
It  is  known  as  the  Mahler- 
Cook  bomb,  and  is  a  modifi- 
cation of  the  Berthelot- 
Mahler  bomb. 

The  Bomb — This  consists 
essentially  of  an  enamel- 
lined  steel  vessel,  capable  of 
withstanding  high  pressures. 
The  lower  part,  D,  is 
closed  by  a  lid,  A,  which  is 
screwed  on,  an  air-tight 
connection  being  obtained 
by  means  of  a  lead-washer, 
C.  Two  stout  platinum 
wires  pass  through  the  cover, 
one,  T,  being  insulated  by 
means  of  a  quartz  plug; 
these  wires  are  connected 
by  two  terminals.  One  of 
the  wires  is  bent  round  in 
the  form  of  a  loop,  so  as  to 

support  a  crucible,  which  may  be  of  platinum,  unglazed  porce- 
lain, or  silica.  The  substance  is  placed  in  the  crucible,  and  the 
ignition  is  effected  by  means  of  a  coil  of  iron  wire,  which  joins 


FIG.  45 


THE  CALORIMETER 


81 


the  two  platinum  wires,  which  is  caused  to  burn  by  means  of 
an  electric  current.  Oxygen  is  admitted  through  a  valve  in  the 
centre  of  the  lid,  the  opening  and  closing  of  the  valve  being 
controlled  by  screw  F.  The  oxygen,  which  is  supplied  from 
a  cylinder  fitted  with  a  pressure  gauge,  is  attached  at  E. 

The  Calwimeter — The  calorimeter  consists  of  a  large  nickel- 
plated  vessel,  A,  to  contain  the  water  in  which  the  bomb  is  to 


FIG.  46 

be  immersed.  This  is  surrounded  by  an  outer  water-jacketed 
vessel.  Both  calorimeter  and  outer  vessel  are  fitted  with 
suitable  stirring  arrangements.  The  stirrer  in  the  calori- 
meter may  be  conveniently  worked  with  a  small  motor.  On 
the  downward  stroke  the  stirrer  should  almost  touch  the 
bottom  of  the  calorimeter,  whilst  on  the  upward  stroke  it 
should  remain  completely  immersed  in  the  water  (see 
Fig.  46). 

The  change  in  temperature  is  read  by  means  of  a  Beckmann 
thermometer.  The  outer  jacket  is  closed  with  a  non-conduct- 
ing lid,  fitted  with  the  necessary  holes  for  stirrer  and  ther- 
mometer. 


82  THERMO-CHEMJCAL  MEASUREMENTS 

The  Water  Equivalent  of  the  whole  apparatus  is  determined 
by  means  of  a  substance  of  known  heat  of  combustion. 

The  heat  received  by  the  water  in  the  calorimeter  can  be 
calculated  from  the  elevation  in  temperature  on  combustion, 
and  from  this  value  and  the  known  heat  of  combustion  of  the 
substance  the  heat  taken  up  by  the  apparatus  can  be  obtained, 
and  hence  the  water  equivalent. 

Camphor,  or  naphthalene,  are  suitable  for  this  purpose,  and 
they  give  out  9292  and  9693  calories  respectively  per  gram 
of  substance. 

Experiment — Open  the  bomb  by  unscrewing  the  nut  B  and 
carefully  remove  the  cover.  Place  a  crucible  in  position. 
Make  a  small  tabloid  of,  say,  camphor ;  weigh  it  accurately 
(use  about  1  gram),  and  place  it  in  the  crucible.  Make  a 
short  spiral  of  about  15  cms.  of  iron  wire,  and  weigh  it,  and 
then  connect  it  between  the  two  stout  platinum  wires.  The 
iron  spiral  is  then  pressed  down  until  it  makes  a  contact  with 
the  substance ;  the  lid  is  then  replaced,  and  the  nut  B  screwed 
tightly  down,  the  bomb  being  held  by  the  bottom  nut,  0, 
which  is  fitted  into  a  hexagonal  plate  fitted  to  the  bench. 
The  bomb  is  then  connected  at  E  with  an  oxygen  cylinder 
and  pressure-gauge.  The  valve  F  is  closed,  and  the  valve  on 
the  oxygen  cylinder  opened  slowly  ;  then  slowly  admit  the 
gas  to  the  bomb  by  opening  F.  When  the  pressure  reaches 
25  atmospheres  with  F  well  open,  close  the  valve  F  tightly, 
and  then  shut  off  the  oxygen  cylinder  and  disconnect. 

The  water-jacket  of  the  calorimeter  should  be  filled  with 
water  several  hours  before  the  experiment  is  to  be  done. 

Weigh  out  into  the  calo'rimeter  about  2-5  kgs.  of  water 
(sufficient  to  immerse  the  bomb  up  to  the  nut  B}.  The 
calorimeter  is  then  placed  in  position,  being  insulated  at  the 
bottom  by  a  wooden  block  or  cork.  To  counterbalance  the 
loss  by  radiation,  the  water  in  the  calorimeter  should  be  at 
a  slightly  lower  temperature  than  that  of  the  room — such 
that  the  temperature  of  the  room  is  the  mean  between  the 
initial  temperature  of  the  water  in  the  calorimeter  and  the 
highest  temperature  of  the  experiment.  The  total  rise  is 
usually  about  3°,  therefore  the  initial  difference  should  be 
about  1'5°.  The  bomb  is  now  carefully  lowered  into  the 
calorimeter  and  the  terminals  connected  to  the  battery,  the 
circuit  being  broken  by  a  switch  key.  Insert  the  Beckmann 
thermometer  and  commence  stirring.  After  about  five  minutes, 


TEMPERATURE  READINGS 


83 


record  the  reading  every  minute  for  about  eight  minutes.  At 
the  eighth  minute  complete  the  electric  circuit,  thereby  causing 
the  ignition  to  take  place.  Continue  to  take  minute  readings. 
When  the  highest  temperature  has  been  reached,  the  readings 
should  be  continued  for  a  further  eight  or  ten  minutes.  The 
observations  are  then  complete.  Open  valve  F  carefully,  and 
then  unscrew  B.  If  any  iron  wire  is  unburnt,  it  must  be  care- 
fully weighed  and  subtracted  from  the  original  weight  of 
iron  used. 

The  method  of  calculating  the  results  will  be  better 
understood  from  the  following  example,  in  which  the  water 
equivalent  of  the  apparatus  is  calculated  by  means  of  naph- 
thalene : 

Weight  of  naphthalene  =  1*2966  grams. 
Weight  of  iron  =  0-1568  gram. 

TEMPERATURE  READINGS 

I 


Time  in  Minutes 

Beckmann  Reading 

±t 

0 

1-805 

_ 

1 

1-808 

0-003 

2 

1-813 

0-005 

3 

1-815 

0-002 

4 

1-818 

0-003 

5 

1-821 

0-003 

6 

1-823 

0-002 

7 

1-824 

o-ooi 

8 

1-825 

o-ooi 

(circuit  closed) 

Mean  =  0-0025 

II 


8 

1-825 

(circuit  closed) 

9 

3-814 

— 

10 

4-536 

— 

11 

4-998 



12 

5-514 

— 

13 

5-666 



14 

5-700 

— 

15 

5-706 

— 

16 

— 

— 

84 


THERMO-CHEMICAL  MEASUREMENTS 


III 


Time  in  Minutes 

Beekmann  Reading 

ft 

16 

5-706                                  — 

17 

5-706 

— 

18 

5-705 

o-ooi 

19 

5704 

o-ooi 

20 

5-703 

o-ooi 

21 

5-703 

o-ooo 

22 

5702 

o-ooi 

23 

5-700 

0-002 

24 

5-697 

0-003 

25 

5-695 

0-002 

26 

— 

— 

Mean  =  0-0011 

During  the  middle  period  (heating  period)  heat  will  have 
been  lost  by  radiation.     From  Series  I  and  III  the  rates  of 


003 
OOZ 
•001 
0 
•001 
•002 
•003 

jt 

/ 

/ 

v 

18      2 

8      3 
/ 

8/  + 

8       5 

8 

/ 

/ 

/ 

FIG.  47 


cooling  can  be  calculated.  In  Series  I  the  rate  of  cooling  is 
negative,  denoting  the  temperature  is  rising — i.e.,  A/  is  nega- 
tive and  8t  positive. 


TEMPERATURE  READINGS 


85 


Draw  a  cooling  curve  as  shown  in  Fig.  47  by  drawing ,  a 
straight  line  through  points  1-8  to  0-0025,  and  5-7  to  0-0011. 
Then  correct  all  temperatures  in  Series  II  from  this  curve. 


Temperature 

Cooling  in  Each 
Minute 

| 

Total  Loss 

Corrected  Tem- 
perature 

1-825 

1 

_ 

1-825 

3814 

-  0-0007 

-0-0007 

3-8133 

4-536 

o-o 

-0-0007 

4-5353 

4-998 

+  0-0004 

-0-0003 

4-9977 

5-514 

+  0-0009 

+  0-0006 

5-5146 

5-666 

+0-001 

+  0-0016 

5-6676 

5700 

+0-0011 

+  0-0027 

57027 

5-706 

+0-0011 

+  0-0037 

5-7097 

The  values  in  the  second  column  are  read  off  from  the 
curve. 

The  corrected  temperature  is  therefore  5*7097  for  the 
maximum.  Hence  the  elevation  =  5-709 7°  -  1*8250°  =  3'8847°. 
The  calorimeter  contained  2500  grams  of  water. 


The  heat  of  combustion 

of  naphthalene          ...     =9,693  cals.  per  gram. 
The  heat  of  combustion 

of  iron 
Therefore   heat   evolved 

by  naphthalene 
Therefore  heat   evolved 


1,600  cals.          „ 

1  2966x9,693  =  12567-9  cals. 


by  iron 
Total  heat  evolved 


=  0-1568x1600  =260-9  cals. 
=  12828-8  cals. 


Of  this,  2500x3-8847  =  9711-9  cals.  were  taken  up  by  the 
water. 

.-.  12828-8  cals.  -9711-9  cals.  =  3116-9  cals. 

Therefore  3116*9  cals.  were  taken  up  by  the  apparatus  in 
rising  3-8847°. 

3116'9 
. -.  Water  equivalent  =  3.3047  =  802-3  grams. 


The  water  equivalent  of  apparatus  =  802 -3  grams. 


86  THERMO-CHEMICAL  MEASUREMENTS 

In  accurate  work  it  is  necessary  to  estimate  the  oxides  of 
nitrogen  which  will  have  been  formed  during  the  combustion, 
and  the  heat  of  formation  allowed  for. 

In  the  above  example  the  water  equivalent  of  the  calori- 
meter was  the  unknown  factor,  the  heat  of  combustion  being 
known.  In  determining  the  heat  of  combustion  the  value 
found  above  will  be  used,  leaving  the  heat  of  combustion  as 
the  only  unknown. 


CHAPTER  XIII 
DETERMINATION  OF  TRANSPORT  NUMBERS 

WHEN  a  current  is  passed  through  an  electrolyte  the 
numbers  of  positive  and  negative  ions  discharged  at  the 
respective  electrodes  in  a  given  time  are  equal.  It  must 
not,  however,  be  assumed  that  the  velocities  of  the  ions 
are  equal,  because  this  is  not  the  case.  The  speed  of  the 
anion  may  be  very  different  from  that  of  the  cation,  and,  in 
fact,  this  is  almost  invariably  so.  The  result  is,  the  con- 
centration of  the  faster  ion  round  the  electrode  towards 
which  it  travels  increases.  This  being  the  case,  Hittorf 
showed  how,  by  experiment,  the  relative  speeds  of  the  ions 
could  be  deduced  from  the  changes  in  concentration  round  the 
electrodes  after  electrolysis.  The  speed  of  the  cation  is 
usually  represented  by  w,  and  that  of  the  anion  by  v.  The 
total  amount  of  electricity  passed  through  the  solution  is 
proportional  to  the  sum  of  the  ionic  velocities — i.e.,  u  +  v.  Of 
this  let  n  be  the  fraction  carried  by  the  anion,  then  1  —  n  will 
be  the  fraction  carried  by  the  cation,  and  from  this  it  follows 
that — 


n  = 


and  1  -  n  — 


u+v  u+v 


The  value  of  n  is  termed  the  transport  number  of  the  anion, 
and  1  -  n  the  transport  number  of  the  cation. 

The  transport  number  can  therefore  be  found  by  deter- 
mining the  total  amount  of  electricity  which  passes  through 
the  solution  and  the  amount  of  one  of  the  ions  which  have 
passed  from  the  solution  in  the  -immediate  neighbourhood  of 
one  of  the  electrodes — i.e.,  determine  the  change  of  concentra- 
tion of  one  of  the  ions  round  one  of  the  electrodes.  Hence,  in 
order  to  investigate  the  changes  of  concentration,  it  is  only 

87 


DETERMINATION  OF  TRANSPORT  NUMBERS 


necessary  to  analyze  a  portion  of  the  solution  round  one  of 
the  electrodes. 

The  above  will  only  be  correct  if  the  liquid  which  is  not  in 
the  immediate  neighbourhood  of  the  electrodes  does  not  alter. 
This  can  be  approximated  too,  if  the  time  during  which  the 
current  passes  is  not  too  long.  The  time  should  also  be  as 
short  as  possible  so  as  to  minimize  the  effect  due  to  diffusion. 
Hittorf  showed  that  the  transport 
numbers  are  practically  independent 
of  the  electromotive  force  between 
the  electrodes.  They  are,  however, 
influenced  by  temperature  to  some 
extent,  and  in  the  case  of  mono- 
atomic  univalent  ions  approach  0*5 
as  the  temperature  rises. 

Experiment  to  Determine  the  Trans- 
port Numbers  of  the  Silver  Ion  and 
the  Nitrate  Ion  in  a  Solution  of  Silver 
Nitrate — The  apparatus  which  is 
best  suited  for  this  purpose  is  Ost- 
wald's  modification  of  Hittorf's  ap- 
paratus (see  Fig.  48) :  two  glass 
tubes,  usually  of  unequal  length, 
connected  near  the  upper  end.  The 
lower  end  of  the  shorter  limb  is 
closed,  while  the  longer  limb  is  pro- 
vided with  a  stop-cock.  Into  the 
tubes  are  fitted,  by  means  of  para- 
ffined corks,  two  electrodes.  The 
one  in  the  longer  limb  is  of  silver, 
made  by  fusing  stout  silver  wire  on 
to  stout  copper  wire,  and  cement- 
ing the  electrode  into  a  glass  tube 
so  that  only  the  silver  is  exposed. 
The  electrode  in  the  shortest  limb  may  be  wholly  of  copper, 
but  it  should  be  enclosed  partly  in  a  glass  tube.  Prior  to  the 
experiment  the  silver  anode  should  be  coated  with  finely 
divided  silver  by  electrolysis  (see  p.  128).  The  shorter  limb, 
which  is  the  anode  compartment,  is  filled  with  a  concentrated 
copper  nitrate  solution  to  just  above  the  exposed  part  of  the 
electrode.  The  rest  of  the  apparatus  is  then  carefully  filled 


FIG.  48 


TRANSPORT  NUMBERS  89 

with  ^r  silver  nitrate  in   such   a   way   that  a   fairly   sharp 

boundary  is  maintained  between  the  copper  nitrate  solution. 
The  cell  is  now  connected  in  series,  with  variable  resistance, 
an  ammeter,  a  copper  voltameter,  and  a  source  of  current, 
such  as  an  electric  lighting  circuit.  The  resistance  must  be 
so  adjusted  that  a  current  of  0*01  ampere  and  a  difference  of 
potential  of  30  to  40  volts  is  passed. 

The  copper  voltameter  may  be  made  up  in  a  glass  cylinder 
as  follows  :  Make  up  a  solution  of  125  grams,  CuS045H2O, 
50  grams  H2S04,  50  grams  of  alcohol,  and  a  litre  of  water. 
Two  copper  electrodes  of  about  2  cms.  square  are  cut  from 
sheet  copper.  The  cathode  must  be  cleaned  and  weighed  at 
the  commencement,  and  then  at  the  end  of  the  experiment  it 
is  washed  first  with  distilled  water,  and  then  with  alcohol,  dried, 
and  again  weighed.  C02  should  be  passed  through  the  volt- 
ameter during  the  experiment. 

When  the  apparatus  has  been  fitted  up  as  indicated,  the 
current  is  passed  for  about  two  to  three  hours.  At  the  end 
of  this  time  the  cathode  of  the  voltameter  is  removed,  and 
weighed  according  to  previous  directions. 

Then  run  off  a  measured  volume  of  about  three-quarters  of 
the  anode  solution,  weigh  it,  and  determine  the  amount  of 
silver  present  by  titration  with  thiocyariate  or  electrolytic 
deposition.  The  remainder  of  the  silver  nitrate  solution  is 
then  run  off,  and  on  analysis  should  have  as  near  as  possible 
the  original  composition.  If  not,  the  experiment  must  be 
repeated  for  a  shorter  period. 

From  the  weight  of  copper  deposit  on  the  voltameter 
cathode  and  the  change  in  silver  concentration  at  the  anode 
the  transport  numbers  can  be  calculated  as  follows  : 

Calculation — Before  the  experiment :  15 '06  grams  of  solution 
contained  0*127  gram  of  silver  nitrate,  which  equals  0*000747 
gram  equivalents  of  silver  for  15*06  grams  of  solution. 

After  the  experiment:  20*28  grams  of  anode  solution  con- 
tained 0*2113  gram  of  silver  nitrate,  which  equal  0*00124 
gram  equivalents  of  silver  for  20-28  grams  of  anode  solution. 

Hence,  before  the  experiment  14*933  grams  of  water  con- 
tained 0*000747  gram  equivalents  of  silver,  after  the  experi- 
ment 20-0687  grams  of  water  contained  0*00124  gram 
equivalents,  ** 


90         DETERMINATION  OF  TRANSPORT  NUMBERS 

If  there  had  been  no  change  in  composition,  20-0687  grams 
of  water  would  have  contained — 

equivalents  of  silver. 

So  the  increase  was  0-00124-  0-001004  =  0-000236  gram 
equivalents  of  silver.  The  weight  of  copper  deposited  in  the 
copper  voltameter  was  0*0145  gram,  or  0*0004602  gram, 
equivalents  of  copper.  Hence  the  amount  of  silver  liberated 
at  the  anode  due  to  the  discharge  of  N03  ions  was  0-0004602 
gram  equivalents  of  silver,  therefore  the  concentration  ought 
to  have  increased  by  this  amount  if  no  silver  had  migrated  to 
the  cathode.  The  amount  which  must  have  migrated  equals — 

0-0004602-0-000236  =  0-0002242  gram  equivalents. 

Now,  the  values  0-000236  and  0-0002242   must  be  pro- 
portional to  the  velocities  of  anion  and  cation  respectively. 
Hence  the  transport  number  for  silver  ion  equals 

0-0002242          M 
1-^Q-QQQ4602  =  0487> 
and  for  N08  ion  — 

0-000236 
n  =  0-0004602  - 


CHAPTER  XIV 
ELECTRICAL  CONDUCTIVITY 

ELECTRICITY  may  be  conveyed  in  two  ways  :  (1)  By  con- 
ductors in  which  there  is  no  transference  of  matter,  as  in  the 
case  of  metallic  conductors  ;  (2)  by  conductors  which  undergo 
simultaneous  decomposition,  as  in  the  case  of  fused  salts  and 
solutions. 

In  the  present  case  we  are  only  concerned  with  the  second 
type  of  conductor. 

Ohm's  Law,  which  holds  for  conductivity  in  general,  may  be 
stated  somewhat  as  follows  :  The  strength  of  an  electric  current 
passing  through  a  conductor  is  proportional  to  the  difference  of 
potential  between  the  two  ends  of  the  conductor,  and  inversely  pro- 
portional to  the  resistance  of  the  latter  —  i.e., 

difference  of  potential  volts 

--  ' 


resstance 
This  is  usually  expressed  symbolically  thus  : 

P    E 
=  K' 

The  standard  of  resistance  is  1  ohm,  and  is  defined  as  the 
resistance  of  a  column  of  mercury  106-3  cms.  long,  and  weighing 
14*4521  grams,  and  the  resistance  measured  at  0°. 

An  ampere  is  that  strength  of  current  which  will  deposit 
0*001118  gram  of  silver  from  a  solution  of  silver  nitrate, 
under  definite  conditions,  in  one  second. 

The  quantity  of  electricity  which  passes  in  one  second  with 
current  strength  of  1  ampere  is  known  as  a  coulomb. 

When  a  current  of  1  ampere  passes  along  a  conductor 
whose  resistance  is  1  ohm,  then  the  difference  of  potential 
between  the  two  ends  of  the  conductor  is  1  volt. 

91 


92  ELECTRICAL  CONDUCTIVITY 

The  unit  of  electrical  energy  is  1  volt  x  1  coulomb,  and  is 
equal  to  107  ergs. 

The  resistance  of  a  conductor  is  proportional  to  its  length 
and  inversely  proportional  to  its  cross  section.  Hence  the 

resistance  R  is  given  by  equation  R  =  /o—  where  p  is  a  con- 

S 

stant.  If  I  and  s  are  each  unity,  then  R  =  p.  The  constant  p  is 
known  as  the  specific  resistance,  and  may  therefore  be  defined  as 
the  resistance  in  ohms  offered  by  a  cube  of  1  cm.  dimensions 
to  a  current  of  electricity.  It  will  be  seen  that  a  conductor 
of  low  resistance  will  have  a  high  conductivity.  Hence 
specific  conductivity  will  be  the  inverse  of  specific  resistance,  and 

therefore  equal  to  -  =  *,  where  K  is  the  specific  conductivity. 

Specific  conductivity  is  measured  in  reciprocal  ohms,  fre- 
quently termed  "  mhos." 

In  dealing  with  solutions,  the  conductivity  does  not  depend 
upon  the  solvent,  but  on  the  solute,  and  it  is  convenient  to 
compare  solutions  containing  quantities  of  solute  proportional 
to  the  respective  molecular  weights. 

By  molecular  conductivity  is  meant  the  conductivity  or  con- 
ductance of  a  solution  containing  1  gram  molecule  of  solute 
when  placed  between  electrodes  of  indefinite  dimensions 
exactly  1  cm.  apart,  and  is  represented  by  /x. 


where  V  is  the  volume  in  cubic  centimetres,  which  contains 
1  gram  molecule  of  solute. 

By  equivalent  conductivity  is  meant  the  conductivity  of  a 
solution  which  contains  1  gram  equivalent  of  solute,  when 
placed  between  two  electrodes  1  cm.  apart.  It  is  usually 
represented  by  A 


where  V  is  the  volume,  which  contains  1  gram  equivalent  of 
solute. 

It  will  be  seen  that  for  such  substances  as  KC1,  which  gives 
rise  to  two  simple  monovalent  ions,  //.  =  A. 

Determination  of  the  Conductivity  of  Electrolytes  —  The 

great  difficulty  in  determining  electrical  conductivities  lies  in  the 
fact  that  by  the  use  of  a  continuous  current  the  products  of 


CONDUCTIVITY  OF  ELECTROLYTES 


93 


electrolysis  accumulate  at  the  two  poles  and  set  up  a  back 
electromotive  force  of  uncertain  value.  This  effect  is  known 
as  polarization.  The  actual  resistance  measured  will  be 
therefore  the  sum  of  the  resistance  of  the  solution  and  the 
polarization  at  the  electrodes.  This  difficulty  was  over- 
come by  Kohlrausch,  who  proposed  the  use  of  an  alternating 
current  instead  of  a  direct  current.  By  this  means  the  polar- 
ization caused  by  the  passage  of  the  current  in  one  direction 
is  removed  before  it  has  time  to  attain  any  appreciable  magni- 


FIG.  49 

tude  by  the  reversal  of  the  current  and  its  passage  in  the 
opposite  direction.  Hence  by  this  means  the  true  resistance, 
and  hence  the  conductivity  of  the  electrolyte,  can  be  deter- 
mined. 

The  most  suitable  mode  of  obtaining  an  alternating  current 
in  the  present  case  is  by  means  of  a  small  induction  coil. 

The  method  usually  employed  to  determine  the  resistance 
of  an  electrolyte  is  the  Wheatstone  bridge  method.  The 
arrangement  of  the  apparatus  is  shown  diagrammaticaily  in 
Fig.  49. 

R  is  a  known  resistance,  S  the  cell  with  platinum  electrodes, 
between  which  the  resistance  of  the  solution  is  to  be  measured; 
a — b  is  a  platinum  wire  (may  be  iridium-platinum  or  nickelin) 
of  uniform  thickness,  which  is  usually  about  a  metre  long,  and 
is  stretched  along  a  scale  graduated  in  millimetres ;  6'  is  a 
sliding  contact.  By  means  of  a  battery  a  direct  current  is  sent 
through  the  coil  L,  thereby  giving  rise  to  an  alternating  current, 


94 


ELECTRICAL  CONDUCTIVITY 


which  divides  into  two  circuits  at  the  contact  (7,  one  part 
going  along  the  circuit  C,  a,  d  through  #,  and  the  other  along 
C,  6,  d  through  the  cells  S.  The  object  of  the  experiment  is  to 
balance  these  two  circuits.  This  is  done  by  means  of  a  sliding 
contact  at  C.  Since  an  alternating  current  is  used,  a  galvano- 
meter cannot  be  used,  so  a  telephone  T  is  connected  to  a — b. 
The  sliding  contact  C  is  moved  along  the  wire  until  there  is 


FIG.  50 


no  sound  in  the  telephone.  When  this  is  the  case,  a  balance 
has  been  made  between  the  two  circuits,  hence  the  points 
a  and  b  must  be  at  the  same  potential.  When  such  circum- 
stances exist,  the  following  relationship  holds — 

E  :  S  : :  a—c  :  c—b ; 

i.e.,  S=E—. 
ac 

Here  R  is  known,  as  cb  and  ac  can  be  measured.  Hence  the 
resistance  of  the  cell  S  can  be  easily  calculated. 

In  actual  experiment  it  is  not  usually  possible  to  obtain 
complete  silence  in  the  telephone,  so  the  point  of  minimum 


CONDUCTIVITY  OF  ELECTROLYTES  95 

sound  is  taken — i.e.,  a  point  such  that  if  the  con  tact  be  moved, 
the  least  bit  either  to  the  left  or  to  the  right  the  intensity  of 
the  sound  is  increased.  The  coil  used  in  these  experiments 
should  be  as  small  as  possible,  so  that  the  amount  of  current 
which  passes  at  each  pulse  is  as  small  as  possible.  The  coil 
may  be  worked  from  a  small  accumulator  or  dry  cell,  but  the 
current  should  be  regulated  with  a  sliding  resistance,  so  that 
the  sound  of  the  coil  can  be  distinctly  heard,  the  vibration 
of  the  hammer  being  quite  uniform.  The  resistance  usually 
takes  the  form  of  the  ordinary  type  of  resistance  box,  the 
various  resistances  being  put  in  circuit  by  the  removal  of 
brass  plugs,  thereby  causing  the  current  to  pass  through  a 
wire  of  definite  resistance ;  the  value  of  each  resistance  being 
indicated  on  the  box. 

Various  types  of  electrolytic  cell  are  used.  Fig.  50  indicates 
two  types.  A  is  a  type  used  for  solutions  of  small  conductivity 
while  B  is  used  for  solutions  of  high  conductivity.  The  elec- 
trodes are  circular  platinum  plates  fitted  with  platinum  wires, 
which  are  sealed  into  glass  tubes.  These  tubes  are  held  in 
position  by  being  fixed  into  the  ebonite  cover  which  closes 
the  cell.  The  electrical  contact  is  made  by  placing  mercury 
in  the  tubes.  The  open  ends  of  the  glass  tubes  attached  to 
the  electrodes  should  be  closed  by  rubber  plugs  when  the 
apparatus  is  not  in  use.  The  bridge,  which  is  represented  by 


TS 


1      1 


FIG.  51 


ab  in  Fig.  49,  is  seen  in  detail  in  Fig.  51.  The  ends  of  the 
wire  are  frequently  held  in  position  by  the  brass  plates,  and 
to  each  of  these  brass  plates  two  terminals  are  fixed.  C  in- 
dicates the  platinum  contact,  which  also  carries  a  connecting 
terminal. 

It  will  be  seen  that  the  actual  length  of  wire  necessary  in 

Tt 

bridge  form  will  depend  upon  the  ratio  ^  -     The  nearer  this  is 

to  unity,  the  nearer  to  the  centre  of  the  scale  will  be  the  final 
position  of  C.  So  that  if  R,  S  are  suitably  arranged,  the 


96 


ELECTRICAL  CONDUCTIVITY 


position  of  C  may  be  confined  to  about  40  or  50  cms.  in  the 
centre  of  the  scale.  Hence  the  actual  bridge  can  be  reduced 
in  length,  and  the  excess  of  wire  wound  round  a  suitable 
drum. 

In  some  special  forms  of  apparatus  modifications  of  this 
type  are  introduced,  and  in  some  cases  the  scale  is  so  graduated 
to  give  directly  the  ratio  of  the  two  resistances  (see  Fig.  52). 


FIG.  52 

It  is  not  advisable  to  rely  upon  the  accuracy  of  the  bridge 
scale,  as  the  wire  is  rarely  absolutely  uniform.  The  motion 
of  the  contact  over  the  wire  also  changes  its  resistance  slightly ; 
so  it  is  necessary  to  calibrate  the  wire  from  time  to  time. 

Calibration  of  the  Bridge  Wire — The  difficulty  of  measur- 
ing the  resistance  of  short  lengths  of  the  wire  lies  in  the  un- 
certainty of  making  a  contact  with  other  wires  which  shall  be 
free  from  resistance.  The  method  usually  adopted  is  that 
devised  by  Strouhal  and  Barus,  which  is  based  on  the  Wheat- 
stone  bridge  principle.  In  this  method  the  resistances  of  the 
contact  do  not  interfere  with  the  measurement.  Ten  approxi- 
mately equal  resistances  are  required,  the  sum  of  which  should 
be  about  the  same  resistance  as  that  of  the  bridge  wire. 
These  resistances  are  in  the  form  of  wire  coils  (Fig.  53) 
soldered  on  to  stout  copper  wire,  and  for  protection  they  are 
mounted  in  glass  tubes.  The  ends  of  the  copper  wire  are 
thoroughly  cleaned  and  amalgamated,  and  arranged  along  a 


CALIBRATION  OF  THE  BRIDGE  WIRE 


97 


board,  as  shown  in  Fig.  54,  the  ends  of  the  copper  wires 
dipping  into  cups  filled  with  mercury,  thus  connecting  up  the 
series.  This  is  then  placed  parallel  to  the  bridge  to  be 


FIG.  53 


FIG.  54 


tested.  The  principle  of  the  method  is  to  find  lengths  of 
wires  at  different  positions  along  the  bridge  which  are  of 
equal  resistance.  The  source  of  current  in  this  case  may  be 
either  direct  or  alternating,  the  exact  compensation  being 


FIG.  55 


detected  by  a  sensitive  galvanometer  in  the  former  case,  and 
by  a  telephone  in  the  latter  case. 

The  bridge  is  then  connected  to  the  resistance  series  by 
stout  copper  leads,  D.     The  whole  arrangement  will  be  under- 
stood from  Fig.  55.      One  of  the  resistance  coils  must  be 
7 


98  ELECTRICAL  CONDUCTIVITY 

chosen  as  a  standard,  and  should  carry  some  suitable  mark  of 
distinction.  It  does  not  matter  which  of  the  coils  is  chosen  as 
the  standard.  The  standard  coil  is  placed  in  cups  1  and  2,  and 
one  of  the  wires  from  the  telephone  placed  in  cup  2  (see 
Fig.  55) ;  then  the  point  on  the  bridge  wire,  where  a  balance 
is  noted.  Now  move  the  standard  coil  to  position  3  without 
changing  the  telephone  wire,  and  again  determine  the  balance- 
point.  The  telephone  wire  is  now  placed  in  cup  3,  and  re- 
determine  the  balance.  The  difference  between  the  last  two 
readings  corresponds  to  a  length  of  the  bridge  wire,  the 
resistance  of  which  is  the  same  fraction  of  the  total  resistance 
of  the  bridge  wire  as  the  standard  is  of  the  sum  of  the  ten 
resistance  coils. 

The  "  standard"  is  now  brought  to  position  3,  4,  the  tele- 
phone wire  being  first  in  3,  and  then  in  4,  and  the  balance 
determined  in  each  case.  This  is  repeated  until  the  standard 
has  reached  position  10,  11,  where  only  one  reading  is  taken 
— i.e.,  with  the  telephone  wire  in  cup  10.  By  this  method 
the  bridge  wire  has  been  divided  up  into  ten  equal  resistances, 
each  of  which  is  equal,  or  approximately  equal,  to  one-tenth 
of  the  whole  resistance.  These  ten  lengths  are  added  together, 
and  the  difference  of  the  sum  from  1000  mm.  divided  by  10, 
and  each  single  value  corrected  by  this  amount,  so  that  now 
the  sum  is  exactly  1000  mm. — i.e.,  the  exact  length  of  the 
bridge  wire,  which,  of  course,  it  must  be  equal  to. 

If  the  single  corrected  values  are  now  added  together  as 
follows,  1,1+2,  1+2  +  3,  and  so  on,  we  obtain  readings 
which  correspond  to  successive  tenths  of  the  wires. 

This  will  be  better  understood  by  studying  the  example 
on  p.  99,  which  is  derived  from  an  actual  experiment. 

It  is  advisable  to  plot  a  graph  from  values  in  the  sixth 
column  of  figures,  so  that  any  intermediate  values  may  be 
approximately  determined. 

Purity  of  the  Water  used  for  Conductivities — It  is  abso- 
lutely essential  that  water  used  in  conductivity  experiments, 
owing  to  the  sensitiveness  of  the  method  of  experiment,  be 
of  a  high  degree  of  purity. 

Water  exhibits  very  different  degrees  of  conductivity, 
depending  upon  the  manner  of  distillation  and  preservation ; 
while  perfectly  pure,  freshly  distilled  water  exhibits  an  ex- 
tremely low  conductivity. 

The  purest  water  so  far  obtained  had  a  specific  conductivity 


CALIBRATION  OF  THE  BRIDGE  WIRE 


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100  ELECTRICAL  CONDUCTIVITY 

of  0-04  x  10~6  reciprocal  ohms  at  18°,  but  water  with  a  con- 

ductivity up  to  3  x  10"  6  reciprocal  ohms  can  be  used  for 
experiments,  in  which  a  fair  degree  of  accuracy  is  re- 
quired. 

The  chief  causes  of  conductivity  are  the  presence  of  small 
quantities  of  carbon  dioxide  and  ammonia. 

The  ordinary  laboratory  distilled  water  is  frequently 
sufficiently  pure  for  ordinary  purposes.  It  can  be  consider- 
ably improved  by  redistillation  in  as  pure  an  atmosphere  as 
possible,  neglecting  the  first  and  last  fractions. 

Where  a  high  degree  of  purity  is  required,  the  condenser 
should,  according  to  Kohlrausch,  be  of  block  tin,  but  fre- 
quently a  Jena  glass  tube  in  the  condenser  is  sufficient.  The 
water  should  be  preserved  in  a  glass  flask  which  has  been 
used  for  a  long  time  to  contain  distilled  water.  The  flask 
should  be  closed  with  a  paraffined  cork  fitted  with  siphon 
tube  and  soda-lime  tube.  If  the  water  contains  much  carbon 
dioxide,  it  may  be  treated  with  baryta  before  distilla- 
tion. 

In  cases  where  absolute  accuracy  is  necessary,  the  con- 
ductivity of  the  water  itself  must  be  determined. 

Determination  of  Cell  Constant  —  The  resistance  of  an  electro- 
lyte must  depend  on  the  capacity  of  the  cell.  By  capacity  is 
meant  the  actual  volume  of  solution  which  is  actually  between 
the  electrodes,  or,  in  other  words,  upon  the  product  of  cross 
section  of  the  electrodes  and  the  distance  between  them.  The 
specific  conductivity,  and  hence  the  specific  resistance,  could 
be  calculated  if  these  two  factors  were  known,  but  it  is  more 
convenient  to  determine  what  is  termed  the  cell  constant,  which 
is  proportional  to  its  capacity.  This  is  done  by  using  an 
electrolyte  of  known  conductivity,  and  a  -£$  normal  solution 
of  potassium  chloride  is  usually  used  for  this  purpose.  As 
before  mentioned  (p.  94)  — 

Rcb 
=  ac' 
Hence  conductivity  — 

I      ac 
==== 


Therefore  C  can  be  determined  by  experiment. 


DETERMINATION ,  OF  CELL  .CONSTANT 


101 


Further,  the  specific  conductivity'  K  must  'be  proportional  to 
the  observed  conductivity — K  =  KG. 


K, 


K  being  the  cell  constant. 
Experiment   to   Determine   the    Cell    Constant    by   Means    of 

^Q  Potassium  Chloride — The  type  of  cell  used  in  this  experi- 
ment should  be  that  with  the  electrodes  near  together 
(Fig.  50,  .4). 

The  experiment  must  be  carried  out  in  a  thermostat  at  25°. 
It  is  essential  that  the  temperature  of  the  thermostat  should 
be  exceedingly  constant,  since  a  change  of  1°  influences 
the  result  2  per  cent.  The  cell,  thoroughly  clean,  is 


FIG.  56 


supported  in  the  thermostat  and  connected  up  by  stout  copper 
wire,  of  negligible  resistance.  The  ends  of  the  wire  must  be 
cleaned  with  emery  paper  so  as  to  give  a  good  contact.  The 
ends  of  the  wire  which  make  a  mercury  contact  (at  the  con- 
ductivity cell)  should  be  amalgamated.  The  arrangement  of 
the  apparatus  will  be  understood  from  Fig.  56. 

The  electrodes  should  be  coated  with  a  uniform  layer  of 
platinum  black  (see  note  at  end  of  chapter),  and  when  freshly 
platinized  they  contain  traces  of  impurity  which  cannot 
readily  be  washed  out,  and  which  would  increase  the  con- 
ductivity. 

To  remove  this,  put  conductivity  water  into  the  cell  to  just 
above  the  electrodes  and  determine  the  resistance  of  the  cell. 


102  ELECTRICAL  CONDUCTIVITY 

Any  soluble  matter  entrained  in  the  platinum  black  will 
slowly  dissolve  out.  Pour  out  the  water  from  the  cell,  put  in 
fresh,  and  again  determine  the  resistance.  Repeat  this  until 
the  resistance  is  constant,  or  only  differs  by  3 — 4  mm.  on  the 
bridge.  Note  this  last  reading,  because  from  it  we  can  calcu- 
late the  conductivity  of  the  water  when  we  have  determined 

the  cell  constant.     Make  up  carefully  a  ^  solution  of  pure 

potassium  chloride.  Wash  the  electrodes  once  or  twice  with 
it.  Then  fill  up  the  cell  to  just  above  the  electrodes,  and  then 
allow  the  solution  to  come  to  the  temperature  of  the  bath. 
Then  determine  the  resistance  of  the  solution.  The  resistance 
put  in  from  the  box  should  be  so  arranged  that  the  reading 
falls  somewhere  between  25  and  75  cms.,  because  an  error  in 
the  readings  at  either  end  of  the  bridge  influences  the  result 
to  a  greater  degree  than  a  similar  error  about  the  middle  of 
the  wire.  Having  determined  the  position  of  minimum  sound, 
change  the  resistance  in  the  box  and  again  determine  the 
balance.  Then  empty  the  cell  and  fill  up  again  with  fresh 
solution  and  repeat  the  above  proceedings.  Calculate  the  cell 
constant  as  indicated  below  from  each  of  the  resistance  read- 
ings, and  take  the  mean  value. 
Given  for  KC1— 

K=  2-768x10-3  at  25°, 

=  2-399x10-3  at  18°, 

=  l-996xlO-3  at  10°, 

expressed  in  reciprocal  ohms. 

Let  R  be  the  resistance  in  the  box,  S  the  resistance  of  the 
cell,  x  the  bridge  reading  in  centimetres,  then 

100 -a;     S       .    g==R(100-s). 

but 

a     _!        .    p  X 

~C  R(lOO-z)' 

Again — 

K  =  p  where  K  =  specific  conductivity. 

.-.K  = 

K  being  the  cell  constant. 


DETERMINATION  OF  MOLECULAR  CONDUCTIVITY     103 

Having  obtained  the  cell  constant,  the  conductivity  of  the 
conductivity  water  can  be  calculated,  for  the  resistance  of  the 
cell  containing  the  conductivity  water  has  already  been  deter- 
mined when  testing  the  electrodes.  The  equation  in  — 

v     K(100-z)R 
K=     ~V~ 

K  is  the  only  unknown,  and  hence  can  be  easily  calculated. 

If  any  difficulty  is  experienced  in  obtaining  a  balance,  it  may 
be  due  to  the  fact  that  sufficient  time  has  not  elapsed  for  the 
cell  to  attain  the  temperature  of  the  bath.  If,  however,  after 
a  reasonable  interval  the  results  are  unsatisfactory,  the  elect- 
rodes should  be  replatinized. 

The  current  should  not  be  allowed  to  pass  through  the  cell 
for  any  considerable  period,  as  this  tends  to  heat  up  the  cell. 

Determination  of  Molecular  Conductivity  and  Degree  of 
lonization  —  If  K  is  the  specific  conductivity  of  a  solution  of 
known  concentration,  then  the  molecular  conductivity  is  given 
by  pv  =  K  V,  V  being  the  volume  which  contains  1  gram  molecule 
of  solute.  If  K  be  determined  for  a  whole  series  of  dilutions 
of  the  original  solution,  the  value  of  ^  will  finally  approximate 
to  /AOO  —  i-V;  molecular  conductivity  at  infinite  dilution. 

It  is,  however,  not  possible  to  measure  the  conductivity  at 
infinite  dilution  with  any  degree  of  accuracy,  so  use  is  made 
of  Kohlrausch's  law,  which  states  that  the  molecular  con- 
ductivity at  infinite  dilution  is  equal  to  the  sum  of  the  veloci- 
ties of  the  ions  — 


where  u  and  v  are  the  speeds  of  the  cation  and  anion  respect- 
ively.    At  any  given  dilution  V  the  formula  will  be  — 


where  a  represents  the  fraction  of  the  molecules  of  the  solute, 
which  is  ionized.  Hence  we  get,  by  dividing  the  second 
equation  by  the  first  — 


that  is,  the  degree  of  dissociation  a  at  any  dilution  is  the  ratio 
of  the  molecular  conductivity  at  that  dilution  to  the  molecular  con- 
ductivity at  infinite  dilution, 


104  ELECTRICAL  CONDUCTIVITY 

Consider,  say,  the  case  of  a  solution  of  acetic  acid  of  concen- 
tration 1,  and  let  a  represent  the  fraction  which  split  up  into 
ions.  Then  the  concentration  of  the  undissociated  portion 


i      ft, 


, 

will  be  represented  by     v     where  V  is  the  volume,  and  the 


concentration  of  each  ion  will  be  y.     Hence,  by  the  law  of 
mass  action,  we  get  — 


or 

'fl^JV 

where  k  is  the  equilibrium  constant. 

Now,  substituting  •*-£•  for  a,  we  get — 

*%oo(fJ^/*v)V' 

A;  is  known  as  the  dissociation  constant  or  ionization  constant. 

The  above  value  is  usually  very  small,  so  K  =  100&  is  usually 
quoted  as  the  dissociation  constant ;  ^^  cannot  be  found 
directly  as  a  rule,  but  has  to  be  calculated  from  the  ionic 
velocities,  as  before  indicated. 

Experiment  to  Determine  the  Molecular  Conductivity  and 
Dissociation  Constant  of  Succinic  Acid — The  apparatus  in  this 
case  is  the  same  as  in  the  former  experiment.  The  cell  and 
electrodes  must  be  clean  and  dry.  The  electrodes  may 
be  conveniently  dried  by  washing  first  with  distilled  water 
and  then  with  pure  alcohol,  and  then  allowed  to  dry  in  a 
warm  atmosphere  free  from  fumes. 

Prepare  T\  molar  solution  of  succinic  acid,  and  place  20  c.c. 
(or  other  convenient  definite  quantity  according  to  size  of  cell) 
of  this  solution  in  the  cell,  in  the  thermostat  at  25°.  When 
solution  has  taken  the  temperature  of  the  bath,  determine  the 
resistance  as  in  previous  experiment,  using  three  different 
resistances  in  the  box.  Now  withdraw  carefully  10  c.c.  (if 
20  c.c.  has  been  used,  otherwise  half  the  original  volume)  of 
solution  from  the  cell,  and  introduce  10  c.c.  of  conductivity 
water  (from  a  stoppered  flask  which  has  been  kept  in  the 


DISSOCIATION  CONSTANT  105 

thermostat).  Mix  the  water  and  solution  thoroughly,  and 
then  determine  the  resistance  again.  Repeat  this  process 
until  the  dilution  reaches  1  gram  molecule  in  10  24  litres  —  i.e.t 
make  six  dilutions.  The  dilutions  are  as  follows  : 

One  gram  molecule  to  16,  32,  64,  128,  256,512,  1024  litres. 
Calculation  — 


=     __  __ 

R  (100-cc)' 
Since  /^  =  /cV, 

_KV        x 
^      R    (100-z)' 

Hence  the  molecular  conductivity  for  various  values  of  V  can 
be  calculated. 

Again,  substituting  the  values  found  for  /^  in  equation— 


£_  „    

given  also  that  IMX  for  succinic  acid  equal  381,  k  can  be  easily 
calculated,  and  also  K  =  100k,  k  being  the  dissociation  constant. 
The  value  k  is  a  very  important  constant,  since  it  is  a 
measure  of  the  strength  or  affinity  of  acids  and  bases.  It  is 
therefore  frequently  called  the  affinity  constant. 

Application  of  Conductivity  Measurements  to  Determine 
Neutralization  Points — Consider  the  case  of  a  dilute  solution  of 
hydrochloric  acid.  According  to  Kohlrausch's  law,  the  conduct- 
ivity depends  upon  the  sum  velocities  of  the  ions — in  this  case 
the  chloride  ion  and  the  hydrogen  ion.  Now,  suppose  a  little 
caustic  soda  is  now  added,  part  of  the  acid  will  be  neutralized. 
This  means  that  some  of  the  hydrogen  ions  have  been  replaced 
by  sodium  ions — viz. : 

H-  +  01'  +  NaOH  =  Na'  +  Cl'  +  H20. 

Now,  the  velocity  of  the  sodium  ion  is  much  less  than  that 
of  the  hydrogen  ion.  Hence  the  effect  will  be  to  reduce  the 
conductivity.  Further,  the  conductivity  will  decrease  until 
the  whole  of  the  acid  has  been  neutralized.  As  soon,  how- 
ever, as  the  neutralization  is  complete,  further  additions  of 
caustic  soda  increase  the  number  of  ions — i.e.,  increase  the 


106  ELECTRICAL  CONDUCTIVITY 

sodium  ions  and  also  introduce  OH'  ions,  therefore  the  con- 
ductivity begins  to  rise  again  ;  and  since  the  OH'  ion  is  very 
mobile,  the  turning-point  is  very  decided. 

Experiment  to  Determine  the  Strength  of  a  Given  Solution  of 
Hydrochloric  Acid — The  manipulation  is  as  in  previous  experi- 
ments. Introduce  into  the  cell  a  known  volume  of  hydro- 
chloric acid  (dilute)  and  determine  the  resistance  as  before. 
Run  in  from  a  burette  small  quantities  of  standard  caustic 
soda,  and  determine  the  resistance  at  each  point.  At  a 
certain  point  the  direction  of  the  movement  of  the  sliding 
contact  will  change.  Then  the  neutralization-point  has  been 
passed.  Make  three  or  four  readings  after  this.  To  deter- 
mine the  exact  neutralization-point  plot  the  bridge  readings 
as  ordinates  against  the  number  of  cubic  centimetres  of  acid 
added.  The  point  of  intersection  of  the  two  curves  thus 
obtained  gives  the  exact  point  of  neutralization. 

This  method  is  of  value  when  dealing  with  highly  coloured 
or  turbid  liquids.  In  the  case  of  weak  acids  use  a  strong 
base,  and  add  the  acid  to  the  base  to  obtain  a  decided  break  in 
the  curve. 

Note  :  Platinizing  Electrodes — Thoroughly  clean  the  electrode 
by  means  of  chromic  acid  solution.  Prepare  also  a  3  per  cent, 
solution  of  chloroplatinic  acid  to  which  0*025  gram  of  lead 
acetate  is  also  added.  Place  the  electrodes  in  the  solution, 
and  connect  up  to  a  4-volt  accumulator.  A  commutator,  or  a 
reversing  switch  must  also  be  in  the  circuit.  Pass  the  current 
for  about  fifteen  minutes,  re  versing  it  every  half -minute,  so  that 
each  electrode  becomes  cathode  and  anode  alternately.  The 
evolution  of  the  gas  should  not  be  too  rapid.  This  may  be 
controlled  by  having  a  sliding  resistance  in  the  circuit. 

Owing  to  the  horizontal  position  of  the  electrodes,  the  gas 
is  very  liable  to  collect  underneath,  thereby  causing  uneven 
distribution  of  the  platinum  black.  This  may  be  avoided  by 
supporting  the  electrodes  in  an  inclined  position.  When 
finished  the  electrodes  should  present  a  fine  velvety  appearance. 
They  still  contain  a  small  amount  of  absorbed  platinizing 
liquid  and  a  small  amount  of  chlorine.  To  get  rid  of  this 
place  the  electrodes  in  dilute  sulphuric  acid,  and  pass  the 
current  for  fifteen  minutes,  reversing  it  every  minute. 

Then  wash  the  electrodes  several  times  in  warm  distilled 
water,  and  then  conductivity  water,  and  finally  preserve  them 
in  conductivity  water  required  for  use. 


CHAPTER  XV 
MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

IN  the  present  chapter  we  are  concerned  mainly  with  the 
study  of  the  relation  between  chemical  and  electrical  energy. 

Electrical  energy,  it  must  be  remembered,  involves  two 
factors,  namely,  the  amount  of  electricity  and  electromotive  force, 
or  fall  in  potential.  Of  these  two  factors  the  latter,  namely, 
electromotive  force,  is  the  more  important,  and  will  be  con- 
sidered in  some  detail  in  the  succeeding  pages. 

When  a  chemical  reaction  takes  place,  the  energy  of  the 
reaction,  or  chemical  affinity,  may  manifest  itself  in  the  form 
of  heat.  Hence  heat  of  reaction  is  frequently  used  as  a 
measure  of  affinity.  Many  reactions,  on  the  other  hand,  give 
rise  to  electrical  energy,  as  in  galvanic  cells ;  in  these  cases  a 
measure  of  chemical  affinity  can  be  obtained  from  a  measure- 
ment of  electromotive  force.  It  must  not  be  assumed  from 
this  that  electromotive  force  is  equal  to  the  heat  of  reaction,  or 
that  electromotive  force  is  a  measure  of  the  heat  of  reaction. 
In  some  cases  they  are  equal,  but  generally  they  are  not  equal. 
The  electromotive  force  is  rather  a  measure  of  the  diminution 
of  free  energy  of  a  system. 

The  relation  between  free  or  available  energy  and  the  heat 
of  reaction  in  a  reversible  reaction  given  by  the  thermodynamical 
equation-  A-U-Q, 

where  A  is  the  free  energy — i.e.,  that  portion  of  the  energy 
which  can  be  transformed  into  work — U  is  the  diminution  of 
the  total  energy  of  the  system  (diminution  of  internal  energy), 
and  Q  is  the  heat  of  the  reaction. 

This  equation  may  be  written  as  a  free  energy  equation — 

A     TJ-T— 
\rr 

107 


108      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

When,  however,  the  chemical  energy  of  the  reaction  is  trans- 
formed into  electrical  energy,  it  is  only  necessary  to  substitute 
the  corresponding  electrical  terms  in  the  above  equation  to 
get  an  expression  of  the  relationship  between  the  chemical 
energy  transformed  and  the  maximum  electrical  energy 
obtainable  in  a  reversible  galvanic  element.  The  resulting 
equation  is  — 


or 


Where  E  is  the  E.M.F.  of  the  cell,  Q  is  the  heat  of  reaction  ; 
for  molar  quantities,  expressed  in  electrical  units,  F  is  96540 
coulombs.  T  is  the  absolute  temperature  at  which  the  cell  is 
working,  n  is  the  valency  or  the  number  of  charges  carried  by  a 

molecule  of  substance  undergoing  change,-^  is  the  temperature 

coefficient  of  the  E.M.F.  Q  has  been  substituted  for  U,  since 
they  are  equal  when  no  external  work  is  done.  A  becomes  wFE 
—  i.e.,  the  maximum  electrical  energy  for  molar  quantities  — 

dA.  .  ._dE 

-Tm  becomes  »BSrfr,  n  and  F  being  constants. 

The  equation  given  above  is  known  as  Helmholtz  equation. 
On  considering  the  equation  in  the  first  form,  it  will  be  seen 
that— 

dE 

(a)  If  ^rp  is  positive,  then  %FE  >  Q,  hence  the  cell  takes  heat 

from  its  surroundings  while  working. 

dft 

(b)  If,  on  the  other  hand,  ^  is  negative,  the  Q  >  ?iFE,  hence 

the  cell  becomes  heated  while  working. 

(c)  If  -™  is  zero,  then  Q  =  nFE  —  i.e.,  the  heat  of  reaction  is 

equal  to  the  electrical  energy,  and  hence  the  temperature  of 
the  cell  remains  unaltered. 

Measurement  of  Electromotive  Force  —  The  most  convenient 
method  of  measuring  the  E.M.F.  of  a  cell  is  by  what  is 
known  as  Poggendorffs  compensation  method.  The  principle 
of  the  method  is  that  the  E.M.F.  of  the  cell  to  be  tested  is 


MEASUREMENT  OF  ELECTROMOTIVE  FORCE      109 

just  compensated  by  the  E.M.F.  of  another  cell  in  the 
opposite  direction,  the  E.M.F.  of  the  latter  being  adjusted  so 
as  to  just  balance  the  cell. 

The  general  arrangement  of  the  apparatus  is  shown  in 
Fig.  57.  A  is  a  source  of  electricity  of  constant  E.M.F., 
such  as,  say,  a  lead  accumulator,  which  is  connected  by  two 
copper  wires  to  the  ends  of  the  uniform  resistance  wire,  B — C, 
which  may  conveniently  be  a  metre  in  length.  The  cell,  E, 
the  E.M.F.  of  which  is  required,  is  connected  through  some 
suitable  measuring  instrument,  such  as  an  electrometer  or 


FIG.  57 

galvanometer,  G,  and  a  tapping  key  to  one  end  of  the  wire 
bridge  at  B,  the  other  pole  being  connected  to  sliding 
contact  D. 

The  point  of  balance  is  found  by  moving  the  sliding 
contact  D  to  a  position  such  as  that  when  the  contact  is  made 
through  the  tapping  key  no  current  passes  through  the 
galvanometer — i.e.,  there  is  no  deflection.  When  such  con- 
ditions hold,  we  have  the  following  relationship  : 

E.M.F.  of  accumulator :  E.M.F.  of  cell  :  :  length  B—C: 
length  B—D— 

•n T\ 

.  - .  E.M.F  of  cell  =  E.M.F.  of  accumulator  x  g_(f 

The  E.M.F.  of  A,  or,  as  it  is  called,  the  working  cell,  is  not 
sufficiently  constant  for  accurate  experiments,  so  it  is  usual 
to  do  a  preliminary  determination  with  a  standard  cell — *.«., 
a  cell  of  known  constant  E.M.F.  in  place  of  E.  Suppose  we 


110      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

find  that  the  standard  cell  balances  at  D',  and  the  cell  to  be 
tested  at  D,  then  we  have — 

B— D'       E.M.F.  of  standard  cell 
B—  D  "unknown  E.M.F.  of  cell  E 

It  is  essential  that  the  E.M.F.  of  the  working  cell  A  should 
be  greater  than  that  of  the  cell  whose  E.M.F.  is  to  be  deter- 
mined. Usually  a  2-volt  accumulator  of  large  capacity,  30  to  40 
ampere  hours,  will  be  found  to  meet  the  requirements.  The 
measuring  wire  B—C  is  usually  the  same  as  described  for 
conductivity  experiments  (p.  95),  and  it  should  be  calibrated 
in  the  same  manner.  If  in  a  metre  wire  the  difference  of 
potential  between  the  two  ends  is  2  volts,  then  1  mm.  on  the 
bridge  will  correspond  to  2  millivolts.  So  that  it  is  easily 
possible  to  get  a  degree  of  accuracy  of  less  than  1  millivolt  of 
error  with  a  fairly  sensitive  galvanometer. 

The  Standard  of  Electromotive  Force — The  standard 
usually  employed  is  the  Westvn,  cell,  the  composition  of  which 
may  be  indicated  as  follows : 

Hg  |  Hg2S04  (solid),  CdS04  (saturated  solution). 
CdS04|H20  (solid),  |  Cd  amalgam  (13  per  cent.  Cd). 

Another  well-known  standard  is  known  as  the  Clark  cell. 
This  cell  has  the  following  composition : 

Hg  |  Hg2S04  (solid),  ZnSO4  (saturated  solution). 
ZnS047H2O  (solid),  |  Zn  amalgam  (10  per  cent.  Zn). 

The  Weston  cell  is  most  frequently  used  now;  it  has  the 
advantage  of  being  easily  reproduced,  and  has  a  very  low 
temperature  coefficient. 

The  cell  itself  usually  consists  of  an  H -shaped  glass  vessel. 

The  vertical  tubes  are  sealed  at  the  bottom  (see  Fig  58). 

Into  one  of  the  limbs  pour  a  layer  of  freshly  distilled  and 
thoroughly  purified  mercury  to  a  depth  of  about  1  cm.  Then 
prepare  a  paste  of  mercurous  sulphate  thus  :  Grind  together 
in  a  mortar  mercurous  sulphate,  a  little  mercury,  and  one  or 
two  crystals  of  cadmium  sulphate,  with  a  little  saturated  solu- 
tion of  cadmium  sulphate.  Filter  through  a  plug  of  cotton- 
wool. Then  rub  the  paste  again  with  a  little  cadmium  sul- 
phate solution,  and  again  filter.  Repeat  this  process  a  third 
time.  The  object  of  this  process  is  to  completely  remove  any 


THE  STANDARD  OF  ELECTROMOTIVE  FORCE     111 

traces  of  mercuric  sulphate.  Place  the  paste  moistened  with 
cadmium  sulphate  solution  thus  prepared  to  a  depth  of  about 
3  mm.  over  the  mercury  ;  then  add  several  large  clear 
crystals  of  cadmium  sulphate.  Into  the  other  limb  place  a 
layer  of  cadmium  amalgam  prepared  as  follows  :  Heat  at  100° 
(say  on  a  water-bath)  7*5  parts  by  weight  of  pure  mercury 
and  1  part  of  cadmium.  Stir  well  with  a  glass  rod.  Heat  up 
the  limb  of  the  cell  in  hot  water,  and  add  the  liquid  amalgam 
to  a  depth  of  about  1  cm.,  then  allow  to  cool,  and  the 
amalgam  solidifies.  On  the  top  of  this  amalgam  place  about 


FIG.  58 

3  mm.  layer  of  finely  powdered  cadmium  sulphate  crystals, 
slightly  moistened.  Then  add  several  large  clear  crystals  of 
cadmium  sulphate,  and,  finally,  fill  up  the  apparatus  within 
about  1'5  cms.  of  the  top  with  a  saturated  solution  of 
cadmium  sulphate.  The  cadmium  sulphate  crystals  used  in 
making  up  the  above  cell  must  have  the  composition 
CdS04|H20,  and  in  preparing  a  saturated  solution  of  the 
salt  the  temperature  should  be  kept  below  75°,  because  above 
this  temperature  the  monohydrate  is  the  stable  phase — i.e., 
CdS04H20. 

The  open  ends  of  the  tube  must  now  be  hermetically  sealed, 
at  the  same  time  an  air  space  must  be  left  in  the  tubes  for 


112      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 


expansion  due  to  rise  in  temperature.  A  small  quantity  of 
clean  paraffin  wax  is  melted,  the  cell  tilted  a  little  to  the  left, 
and  the  paraffin  wax  poured  carefully  on  to  the  surface  of  the 
solution  in  the  left-hand  limb  to  a  depth  of  about  0*5  cm. 
The  tube  is  then  tilted  to  the  right,  and  the  right-hand  tube 
treated  in  the  same  way.  On  the  top  of  the  paraffin  place  a 
layer  of  cork  O5  cm.  thick,  and,  finally,  close  the  tube  with  the 
sealing  wax.  In  the  above  cell  the  mercury  is  the  positive 
pole,  and  the  amalgam  the  negative  pole.  The  E.M.F.  of  the 
Normal  Weston  cell  is  practically  independent  of  temperature, 
as  it  only  changes  -0-00004  volt  per  degree  for  the  range 
15°  to  20°. 

THE  E.M.F.  AT  TEMPERATURES  FROM  0°  TO  30° 


Temperature 

E.M.F.  in  Volts 

0° 

1-0189 

5° 

1-0189 

10° 

1-0189 

15° 

1-0188 

20° 

1-0186 

25° 

1-0184 

30° 

1-0181 

Generally  for  a  temperature  t°. 
Ee  =  1  '0186  -  0-00004  (t°  -  20)  nearly. 

For  ordinary  room  temperatures  we  may  take  the  E.M.F. 
as  1-019  volts.  Care  must  be  taken  not  to  short  circuit  the 
cell,  as  this  changes  slightly  the  E.M.F.,  since  it  causes  some 
solid  Hg2S04  to  go  into  solution,  and  it  takes  some  time  for 
the  cell  to  recover  its  normal  condition.  It  is  also  advisable 
to  enclose  the  cell  in  an  opaque  case. 

The  Clark  cell  only  differs  from  the  Weston  in  that  zinc  is 
substituted  for  cadmium  in  each  case. 

The  temperature  coefficient  of  the  Clark  cell  is  higher  than 
that  of  the  Weston,  as  will  be  seen  from  the  following  equa- 
tion, which  gives  the  value  of  the  E.M.F.  at  any  tempera- 
ture (f)  : 

E«=  1-433  -0-0012  (f  -15°)  very  nearly. 

In  the  experimental  determination  of  E.M.F.  it  is  found 


CAPILLARY  ELECTROMETER 


113 


much  more  convenient  to  use  a  capillary  electrometer  instead  of 
a  galvanometer. 

Capillary  Electrometer— The  most  convenient  form  of 
electrometer  for  common  use  is  what  is  known  as  the  open 
form  of  capillary  electrometer,  a  useful  design  of  which  is 
indicated  in  Fig.  59.  It  consists  of  two  fairly  wide-bored 
tubes,  one  having  a  bulb  at  one 
extremity ;  these  two  tubes  are 
joined  together  by  a  fine  capillary 
tube.  Pure,  clean,  dry  mercury 
is  poured  into  limb  A  until  the 
mercury  stands  just  over  halfway 
up  the  fine  capillary  tube ;  then 
the  bulb  of  limb  B  is  filled  to  about 
halfway  with  mercury ;  the  rest 
of  the  tube  B  is  filled  with  dilute 
sulphuric  acid  (1  part  sulphuric 
acid  to  6  parts  of  water),  which 
had  been  previously  agitated  with 
a  little  pure  mercury.  The  sul- 
phuric acid  should  make  a  clean 
junction  with  the  mercury  in  the 
capillary.  To  do  this  blow  down 
tube  A  until  a  little  mercury  has 
been  drawn  over  into  B.  On  re- 
leasing the  pressure,  the  sulphuric 
acid  will  be  drawn  back  into  the 
capillary.  It  is  sometimes  neces- 
sary to  suck  at  tube  A  in  order 
to  bring  the  sulphuric  acid  back, 
but  care  must  be  taken  not  to  get  the  sulphuric  acid 
round  the  bend.  A  platinum  wire  passes  down  tube  B,  making 
contact  with  the  mercury;  the  wire  is  insulated  from  the 
sulphuric  acid  by  means  of  a  glass  tube.  Contact  is  made  in 
limb  A  by  means  of  a  piece  of  platinum  wire. 

It  is  essential  that  in  using  the  capillary  electrometer  the 
sulphuric  acid  limb  should  be  connected  with  the  positive 
pole,  and  the  mercury  limb  with  the  negative  pole.  If 
they  are  connected  in  the  reverse  way — i.e.,  the  mercury 
limb  made  the  anode — the  mercury  would  go  into  solution, 
giving  rise  to  mercurous  sulphate  in  the  capillary,  which 
would  dirty  the  tube,  thereby  causing  the  mercury  to  stick 


FIG.  59 


114       MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

and  give  fallacious  results.  If  this  should  happen  by  acci- 
dent, and  another  electrometer  is  not  available,  it  should  be 
thoroughly  cleaned  out  with  a  hot  solution  of  potassium 
bichromate  and  sulphuric  acid,  followed  by  several  washings 
with  distilled  water,  and  finally  dried  with  filtered  air.  It 
may  then  be  filled  as  before  described. 

Principle  of  the  Capillary  Electrometer— When  mercury  and 
sulphuric  acid  in  a  capillary  tube  are  connected  in  the  manner 
mentioned  above  with  some  source  of  electromotive  force,  the 
area  of  separation  between  the  liquids  in  the  capillary 
diminishes.  This  is  due  to  a  change  in  the  potential  difference 
between  the  two  liquids. 

CirCU*  Elecrromerer  Elecfromerer 
Circu^ 


Circuit- 
Circuit 


E  lee  from  erer 

FIG.  60 

A  certain  amount  of  mercury  dissolves  in  the  sulphuric 
acid,  giving  rise  to  mercurous  sulphate.  Now,  the  osmotic 
pressure  of  the  solution  of  mercury  salt  will  be  greater  than 
the  solution  pressure  of  the  mercury,  hence  positive  mercury 
ions  from  the  solution  will  be  deposited  on  the  surface  of  the 
mercury,  and  this  surface  will,  as  the  result  of  this,  become 
positively  charged  with  regard  to  the  solution ;  then  in  all 
probability  this  positively  charged  surface  holds  a  correspond- 
ing negative  layer  near  the  surface  of  the  acid,  thus  giving  a 
sort  of  Helmholtz  double  layer. 

Another  factor  has  also  to  be  considered — namely,  surface 
tension.  The  effect  of  surface  tension  is  to  tend  to  make  the 


PRINCIPLE  OF  CAPILLARY  ELECTROMETER       115 


surface  area  as  small  as  possible.  The  attraction  between  the 
two  oppositely  charged  layers  will  tend  to  counteract  this 
effect ;  in  other  words,  diminishes  the  surface  tension. 

In  actual  experiment  the  two  poles  of  the  electrometer 
must  be  connected  so  as  to  bring  the  two  surfaces  to  the  same 
potential  difference  before  any  measurement  is  made.  This  is 
achieved  by  means  of  a  triple 
contact  Morse  key  (Fig.  60). 
Now,  if  any  increase  or  de- 
crease charge  be  brought 
about  from  outside  sources, 
then  the  concentration  of  the 
ions  in  the  immediate  neigh- 
bourhood of  the  mercury 
alters  by  causing  some  mer- 
cury to  either  pass  into  solu- 
tion or  else  be  deposited.  The 
effect  of  this  is  to  alter  the 
potential  difference,  and  hence 
the  surface  tension,  thereby 
causing  the  mercury  thread 
to  rise  or  fall  in  the  capillary 
tube  ;  therefore  when,  on  put- 
ting the  electrometer  into 
circuit,  no  movement  occurs 
in  the  capillary  tube,  there 
is  no  difference  of  potential 
— i.e.,  both  sides  balance. 

This  form  of  electrometer 
was  devised  by  Lippman,  and 
is  therefore  known  as  Lipp- 
irian's  Electrometer. 

The    advantages     of     this 
electrometer   consists    in    its 
action  being  practically  astatic  one,  no  current  being  taken 
from  the  element  operating  it. 

In  any  experiment  the  object  is,  of  course,  to  find  the  point 
at  which  the  level  of  the  mercury  remains  stationary,  for  then 
the  two  opposing  potentials  balance.  If  a  high  degree  of 
accuracy  is  required,  it  is  necessary  to  observe  the  meniscus 
of  the  mercury  by  means  of  a  microscope,  because,  for  small 
differences  of  potential,  the  meniscus  alters  only  very  slightly, 


FIG.  61 


116      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

and  cannot  be  accurately  observed  with  the  naked  eye.  The 
electrometer  and  microscope  are  mounted  on  a  suitable  stand  ; 
the  electrometer  should  be  illuminated  by  a  mirror  or  diffused 
light  from  a  suitably  protected  electric  lamp.  The  apparatus 
is  usually  sold  complete  by  the  makers  (see  Fig.  61).  The 
eyepiece  contains  a  graduated  scale,  by  means  of  which  the 
rise  and  fall  of  the  meniscus  can  be  measured.  With  the  aid 
of  a  microscope,  the  electrometer  is  sufficiently  accurate  to 
detect  0-0001  of  a  volt. 


FIG.  62 


Experiment  Standardization  of  Weston  Cell — The  Weston 
cell,  prepared  according  to  the  directions  already  given,  must 
be  compared  with  some  other  known  standard  cell.  The 
apparatus  is  fitted  up  as  shown  in  Fig.  62.  A  is  the  working 
cell  connected  to  the  end  of  bridge  wire  B — 0;  E  a  capillary 
electrometer;  Tlt  T2  are  connecting  terminals  ;  K  is  a  Morse 
tapping  key  ;  Sl  is  the  known  standard,  and  S2  the  standard 
to  be  tested,  they  are  put  in  circuit  separately,  as  required, 
by  means  of  a  two-switch,  P  ;  D  is  the  sliding  contact  on  the 
wire  bridge.  It  is  also  advisable  to  insert  a  plug,  M,  so  that 
the  accumulator  can  be  easily  disconnected. 

Make  sure  all  connections  are  clean,  and  give  a  good  con- 
tact ;  then  put  in  circuit  the  known  standard  S1  ;  allow  the 


SINGLE  POTENTIAL  DIFFERENCES  117 

current  to  flow  along  the  bridge  wire  by  inserting  plug  M\ 
move  the  sliding  contact  to  just  past  the  middle  of  the 
bridge  ;  press  down  the  Morse  key  sharply,  and  observe 
through  the  microscope  the  movement  of  the  mercury  men- 
iscus in  the  electrometer. 

If  the  mercury  appears  to  go  down  in  the  microscope—  i.e., 
in  reality  it  moves  up  —  then  move  the  sliding  contact  down  a 
little  until  a  point  is  found  where  the  mercury  begins  to  move 
in  the  opposite  direction.  The  null-point  of  the  electrometer 
is  between  these  two  readings.  Now  move  the  sliding  contact 
a  few  millimetres  at  a  time  until  the  motion  of  the  mercury 
meniscus  is  again  reversed.  Repeat  this  process  until  a  point 
is  found  such  that  a  slight  movement  of  the  sliding  contact 
either  one  way  or  the  other  causes  the  meniscus  to  move  in  the 
opposite  direction.  At  the  point  itself  the  meniscus  should 
not  move  at  all  on  pressing  the  tapping  key.  As  a  check  on 
the  above  result,  find  two  points  1  mm.  apart  such  that  they 
give  opposite  directions  to  the  motion  of  the  meniscus  ;  then 
measure  the  extent  of  the  movement  at  both  points  by  means 
of  the  scale  in  the  eyepiece,  and  calculate  the  exact  position 
of  the  balance  by  proportion.  As  the  point  of  balance  is 
approached,  it  will  be  necessary  to  keep  the  Morse  key 
depressed  several  seconds  before  any  movement  may  be 
detected.  Now,  having  determined  the  balance-point  for  Sv 
alter  the  two-way  switch  so  as  to  put  S2  in  circuit  instead  of 
Sv  and  repeat  the  above  process. 

Then,  if  B—  D  be  the  reading  for  S,  and  B—  Dl  for  Sv 
we  have  — 

E.M.F.  of  Sl     B—D 


or 

E.M.F.  of 


Measurement  of  Single  Potential  Differences  —  When  a 
metal  is  dipped  into  a  liquid,  it  possesses  a  certain  definite  solu- 
tion pressure,  so  that  the  metal  tends  to  dissolve  ;  it  can,  how- 
ever, only  dissolve  in  the  ionic  form,  hence  it  sends  into 
solution  a  number  of  positively  charged  ions.  The  solution 
therefore  becomes  positively  charged,  and  the  metal  must 
acquire  the  corresponding  negative  charge.  An  electric  double 
layer  is  then  found,  and  a  state  of  equilibrium  is  ultimately 


118      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

reached,  when  the  electrostatic  action  of  the  double  layer  just 
balances  the  solution  pressure  of  the  metal.  If,  however,  the 
liquid  contains  already  a  dissolved  salt  of  the  metal,  the  solu- 
tion will  already  contain  positive  ions  of  the  metal,  and  these 
positively  charged  ions  will  resist,  by  virtue  of  their  osmotic 
pressure,  any  increase  of  metallic  ions  by  solution  of  the 
metal.  In  this  way  a  potential  difference  is  set  up  between 
the  metal  and  the  solution,  which  will  be  equal  to  the  differ- 
ence between  the  solution  pressure  of  the  metal  and  the 
osmotic  pressure  of  the  ions  in  the  solution.  It  will  be  clear 
that  the  relative  charges  on  the  metal  and  solution  will  depend 
on  the  relative  values  of  the  solution  pressure  of  the  metal  and 
the  osmotic  pressure  of  the  ions  in  solution. 

Let  P  be  the  solution  pressure  of  the  metal,  and  p  the 
osmotic  pressure  of  the  ions  in  the  solution.  Then,  if — 
(a)  P  > pt  the  metal  sends  ions  into  the  solution  until  a 
balance  is  obtained;  the  metal  will  then  be  negatively 
charged  and  the  solution  positively  charged. 

(b)  P<p  positive  ions  from  the  solution  will  be  deposited 
on  the  metal  until  the  electrostatic  attraction  balances  the 
osmotic  pressure,  thus  the  metal  will  be  positively  charged 
and  the  solution  negatively  charged. 

(c)  P  —p.     In  this  case  no  change  occurs,  and  no  difference 
of  potential  between  the  metal  and  solution  results. 

The  alkali  metals  (iron,  zinc,  etc.)  belong  to  case  (&),  and 
mercury,  silver,  copper,  etc.,  belong  to  case  (b). 

The  amount  of  the  charge  can  be  calculated  by  considering 
the  maximum  work  which  is  obtainable  when  a  molecule  of  the 
metal  at  a  solution  pressure  P  passes  into  ions  of  osmotic 
pressure  p. 

On  the  assumption  that  the  changes  at  the  junction  of 
metal  and  solution  are  reversible,  then  we  have  the  osmotic 
work — 

A=RTlog.|; 

but  A  =  wFE,  where  n  is  the  valency  of  the  metal,  and 
F  =  96540  coulombs. 

.•.wFE  =  KTlogeJ, 
or  RT 


CALOMEL  ELECTRODE 


119 


Now,  R=l-99  cals.  and  1  volt  coulomb  =  0'239  cal. 
.•.  R  =  8*316,  expressed  in   electrical   units.     Reducing   to 
ordinary  logs  by  multiplying  by  2 '302 6,  we  get — 

0-0001983  P 

-^ 

At  room-temperature  (15°  to  20°)  the  equation — 

0-058   .         P 
^-'lo^0p 

is  usually  taken,  and  it  should  be  remembered  in  that  form. 

The  system,  which  consists  of  a  metal  dipping  in  a  solution 
of  one  of  its  salts,  is  termed  a  half -element. 

The  measurement  of  the  potential  between  the  electrode 
and  the  solution  can  only  be  done  by  comparing  it  with 
another  electrode  and  solu- 
tion whose  potential  differ- 
ence is  known.  The  method 
is  to  fit  up  a  cell  one  of  the 
electrodes,  of  which  is  the 
standard  electrode  of  known 
E.M.F.,  and  the  other,  the 
electrode  the  E.M.F.  of  which 
is  desired ;  then  the  unknown 
E.M.F.  will  be  the  difference 
between  the  E.M.F.  of  the 
cell  and  the  E.M.F.  of  the 
standard  half-element.  The 
most  suitable  form  of  standard 
electrode  is  the  calomel  half- 
element,  which  will  now  be 
described. 

Calomel  Electrode  —  The 
apparatus  may  be  somewhat  as 
shown  in  Fig.  63.  It  consists 
of  a  glass  tube  about  3-5  cms. 
wide,  fitted  on  one  side  with 
a  short,  straight  tube,  D,  and  on  the  other  side,  about 
halfway,  is  attached  a  tube,  C,  bent  twice  at  right  angles. 
The  open  end  of  tube  C  is  drawn  out  so  as  to  somewhat  con- 
strict the  opening.  The  apparatus  should  be  thoroughly 


FIG.  63 


120      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

cleaned  with  hot  solution  of  potassium  bichromate  and 
sulphuric  acid,  and  washed  with  distilled  water  several  times, 
and  then  dried  by  directing  a  stream  of  hot  filtered  air 
into  the  tube  ;  then  about  2  c.c.  of  pure  dry  mercury  are 
poured  into  the  bottom  of  the  tube.  Prepare  a  normal  solu- 
tion of  potassium  chloride  (pure  recrystallized) ;  then  prepare 
a  calomel  paste  as  follows  :  Rub  well  together  in  a  mortar 
calomel  and  pure  mercury  and  a  little  of  the  potassium 
chloride  solution,  allow  the  mixture  to  settle,  then  decant  off 
the  solution  ;  add  a  further  portion  of  potassium  chloride,  and 
again  work  up  the  mixture  in  the  mortar ;  once  more  decant 
off  the  solution.  Repeat  the  above  operation  a  third  time ; 
then  add  a  portion  of  calomel  paste  thus  prepared  to  the  bulk 
of  the  potassium  chloride  solution,  and  shake  the  mixture  in 
order  to  saturate  the  solution  with  calomel.  Then  decant  off 
the  clear  solution  for  future  use.  Then  with  the  remainder  of 
calomel  paste  make  a  layer  of  2  to  3  mm.  over  the  mercury. 
Then  fill  up  the  tube  to  just  about  the  point  where  tube  C  joins 
tube  A.  The  connection  with  the  mercury  is  made  by  means 
of  a  platinum  wire  sealed  in  a  glass  tube,  JB,  the  electrical  con- 
nection being  made  by  pouring  a  little  mercury  into  the  tube 
and  inserting  an  amalgamated  copper  wire.  The  tube  B  is 
held  in  position  by  a  paraffin  cork,  which  closes  the  top  of  the 
cell.  When  a  measurement  is  to  be  made,  the  side  tube  C 
must  also  he  filled  with  the  calomel-saturated  potassium 
chloride  solution.  This  is  done  by  immersing  the  end  of 
tube  C  in  the  solution  and  applying  suction  at  D  (to  which  a 
short  rubber  tube  is  attached),  and,  when  C  is  completely  full, 
closing  D  by  means  of  a  clip.  The  calomel  electrode  is  termed 
the  absolute  standard,  and  has  a  potential  difference  of  0*560 
volt  at  18°  between  the  mercury  and  the  solution. 

•  The  great  advantage  of  the  calomel  electrode  as  a 
standard  is  that  it  can  be  reproduced  with  a  high  degree 
of  accuracy. 

Use  of  Calomel  Electrode  to  Determine  Electrode :  Potentials 
— Suppose  it  is  required  to  determine  the  potential  difference 
between  metal  and  solution  when  zinc  is  dipped  into  a  normal 
solution  of  zinc  sulphate,  then  the  zinc  electrode  (see  later, 
p.  122)  is  combined  with  the  calomel  electrode  to  form  a  cell. 
The  E.M.F.  of  the  cell  is  then  determined  by  means  of  bridge 
wire,  and  is  found  to  be  1-076  volts.  Now,  zinc  is  negative 
with  respect  to  mercury,  so  that  the  current  goes  from  zinc 


CALOMEL  ELECTRODE  121 

to    mercury    in    the    cell.       This    may    be    represented    as 
follows  : 

Zn  InZnSOJIHftCl,!  Hg. 


1-076 

We  know,  however,  that  positive  electricity  tends  to  pass 
from  the  solution  to  the  mercury,  and  the  difference  of 
potential  is  0*560  volt. 

Zn|7iZnS04||Hg2Cl2|  Hg. 
TiKCl 


0-560 


1-076 

From  this  it  is  obvious  that  the  potential  difference  between 
the  zinc  and  the  zinc  sulphate  must  be  1-076  volts -0'56  volt 
=  0-516  volt. 

Zn  |  wZnSO4 1|  Hg^  |  Hg. 
nKCl 

0-516  0-56 

1-076 
Consider  cell : 

Cu  |  wCuSOjIHggCVraKCl  |  Hg. 

Copper  is  positive  with  respect  to  mercury,  hence  the  elec- 
tricity flows  from  mercury  to  copper  in  the  cell.  The  current 
in  each  electrode  tends  to  flow  from  solution  to  the  metal — 
i.e.,  in  opposite  directions— hence  the  E.M.F.  of  the  cell  will 
be  the  difference  between  the  actual  potentials  of  the  two 
electrodes.  The  E.M.F.  of  the  cell  is  0-025  volt,  hence 
Cu  |  ?iCuS04  junction  the  E  M.F.  is  0-585  volt. 

Cu  |  «CuSOJ|Hg2Cl2.wKCl  |  Hg. 
0-585  0-560 

0-025 


122      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

From  these  two  examples  we  see  that  the  cell  Zn  |  wZnS04 
||wCuS04  |  Cu  ought  to  have  an  E.M.F.  of  0-516  +  0-585  =  1-101 
volts,  this  is  in  agreement  with  experimental  fact. 


Zn     wZnS0     wCuS0      Cu. 


0-516  0-585 

rioi 

Generally,  the  total  E.M.F.  of  a  cellis  equal  to  the  algebraic  sum 
of  potential  differences  of  the  two  electrodes. 

Preparation  of  Zn  |  nZnS04  and  nCu  |  CuS04  Electrodes— 
The  glass  portion  of  the  electrode  is  identical  with  that 
described  for  the  calomel  electrode.  Then  pieces  of  pure  zinc 
and  copper  rod  about  3-5  cm.  long  are  soldered  to  fine  insulated 
copper  wire.  These  are  then  mounted  in  glass  tubes  by  means 
of  sealing-wax  or  cement,  so  that  the  junction  is  not  exposed 
—  i.e.,  only  the  rod  of  pure  metal  projecting  out  of  the  tube  to 
a  length  of  2-5  to  3  cm.  It  is  now  necessary  to  prepare  the 
surfaces  of  these  electrodes.  In  the  case  of  zinc  electrodes, 
they  are  first  cleaned  by  dipping  in  dilute  sulphuric  acid  and 
then  the  surface  amalgamated  by  rubbing  mercury  over  the 
surface  with  a  piece  of  cotton-wool.  Having  got  a  uniform 
surface,  the  electrodes  are  then  thoroughly  washed  with  dis- 
tilled water. 

Copper  electrodes  must  be  coated  with  a  fine  deposit  of 
electrolytic  copper.  First  clean  the  surface  of  the  copper  by 
dipping  in  nitric  acid,  and  then  wash  it  with  distilled  water  ; 
then  make  up  a  copper  solution,  having  the  following  con- 
stituents in  the  proportions  indicated  : 

CuS045H20  125  grams 

H2S04     .........  50      „ 

Alcohol  ...  ...  ...  50      „ 

Water     ...  ...  ...  1000      „ 

Then  make  the  electrode  the  cathode  and  a  strip  of  copper 
the  anode  ;  pass  a  current  of  density  0-5  amperes  per  100  sq.  cm. 
The  electrode  is  thereby  coated  with  a  fine  deposit  of  copper. 
If  the  current  density  used  is  too  high,  the  deposit  will  be  too 
coarse,  and  will  not  adhere  properly.  Two  electrodes  of  each 
kind  should  be  made,  and  each  pair  tested.  The  electrodes 


ELECTRODE  POTENTIALS 


123 


are  then  fitted  into  a  paraffined  cork ;  the  tubes  are  filled  with 
solutions  of  normal  copper  sulphate  and  normal  zinc  sulphate 
respectively.  Now  compare  two  zinc  electrodes.  Fit  them 
up  as  shown  in  Fig.  64 ;  then  fit  up  apparatus  as  used  for 
testing  standard  cell  (Fig.  62),  substituting  the  above  cell  for 
S2,  but  connect  the  cell  in  series  with  Sv  not  in  parallel,  as 
before.  Now,  as  before,  determine  the  point  of  balance  with 
the  standard  cell  alone  ;  then  move  the  two-way  switch  so 
that  both  the  cells  are  in  circuit,  and  again  determine  the  zero 
If  both  zinc  electrodes  are  identical,  then  there  should  be  no 
change  in  the  zero.  It  frequently  happens  that  there  is  a 
slight  change  in  the  zero — i.e.,  a  slight  E.M.F.  in  the 


FIG.  64 

Zn  |  »ZnS04  cell.  This  may  be  got  rid  of  by  joining  up  the 
two  electrodes  with  a  copper  wire  and  short  circuiting  until 
there  is  no  E.M.F.  The  copper  electrodes  should  be  tested  in 
a  similar  manner. 

Experiment:  Determination  of  the  Difference  of  Potential 
between  Copper  and  a  Normal  Solution  of  Copper  Sulphate — 
Prepare  the  Cu  |  nCuS04  electrode  as  previously  described. 
Complete  the  cell  by  combining  the  copper  electrode  with  a 
calomel  electrode  by  means  of  three  times  normal  potassium 
chloride  (potassium  chloride  or  nitrate  solutions,  fairly  concen- 
trated, and  are  frequently  used  to  eliminate  contact  potential, 
which  would  result  at  the  junction  of  the  two  liquids).  Fit 


124      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

up  the  apparatus  as  indicated  in  Fig.  65.  E,  the  capillary 
electrometer,  is  connected  up  as  previously  described ;  Sl  is 
the  Weston  cell;  S2  the  Cu  |  rcCuS04  |  KC1  |  Hg2Cl2rcKCl  | 
Hg  cell. 

The  cells  £  and  S2  are  connected  in  series.  If  a  three-way 
key  is  available,  it  may  be  substituted  with  advantage  for  the 
two-way  key  indicated  in  previous  experiments. 

Now  put  the  Weston  cell  only  in  the  circuit,  and  determine 
the  point  of  balance  by  moving  the  sliding  contact  D.  Note 


M 


FIG.  65 


the  reading.  Now  put  the  unknown  cell  in  circuit  as  well, 
and  redetermine  the  point  of  balance.  If,  however,  it  is 
impossible  to  find  a  balance,  no  matter  what  the  position  of 
the  contact  D  is,  the  wires  attached  to  the  unknown  cell  must 
be  interchanged,  since  the  above  result  was  due  to  the  positive 
pole  of  the  cell  being  connected  with  the  contact  D.  It  will 
now  be  found  possible  to  obtain  a  balance.  Note  the  reading. 
The  first  reading  corresponds  to  the  E.M.F.  of  the  Weston 
cell,  and  the  second  reading  to  the  E.M.F.  of  Weston  +  the 
E.M.F.  of  S2.  The  readings  will  be  proportional  to  the 
E.M.F. 's  in  the  two  cases — i.e., 

E.M.F.  of  Weston  +  S9    x, 


E.M.F.  of  Weston 


x2 


where  x1  is  the  reading  for  Weston  +  S2  and  x2  for  Weston 
alone. 


ELECTRODE  POTENTIALS  125 

Now,  the  E.M.F.  of  the  Weston  has  been  already  found,  say, 
1-019  volts;  hence  we  get  — 

E.M.F.  of  S2  =  (j±  x  1-019)  -  1-019. 

The  E.M.F.  of  S2  is  very  small,  as  before  mentioned,  being 
about  0-025  volt,  and  that  is  the  reason  why  in  this  case  the 
cells  were  connected  in  series  —  i.e.,  because  if  S2  had  been  put 
in  circuit  alone,  the  ratio  of  the  E.M.F.  of  S2  to  that  of  the 
working  cell  A  would  have  been  such  as  to  cause  the  balance 
to  come  very  near  the  end  of  the  scale,  and  hence  the  result 
would  have  been  very  unreliable.  Having  determined  the 
E.M.F.  of  /S2,  and  knowing  the  difference  of  potential  for 
the  calomel  electrode,  the  difference  of  potential  for  the 
Cu  |  «CuSO4  can  be  calculated.  Care  must  be  taken  in  noting 
the  algebraic  sign. 

For  example  — 

Cell       Cu  |  7iCuSO4    Calomel 

0-025=          x  +(-560) 

.-.  z-0-585. 

Experiment  :  Repeat  the  Above  Experiment,  substituting 
Zn  |  nZnSOt  Electrode  for  the  Cu  \  nCuSO^  Electrode—  In  this 
case  the  cells  Sl  and  &  should  not  be  connected  in  series,  but 
put  in  the  circuit  independently,  as  the  E.M.F.  of  the  cell 
Zn  |  nZnS04  |  3nKC\  \  Hg2CL  |  Hg  is  sufficient  to  give  a 

nKCl 
satisfactory  bridge  reading  alone  — 

T,  E.M.F.  of  Weston    xl 

E.M.F.  of  S       =' 


xl  being  the  reading  when  Weston  is  in  circuit,  and  x2  when 
S2  is  in  circuit. 

E.M.F.  of  S2  =  E.M.F.  of  Weston  x^. 
E.M.F.  of  S2  =  1-019  x  ^  volts. 

The  result  should  be  about  T08  volts.     From  this  calculate 
the  electrode  potential  as  before. 


126      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

In  the   same  way  determine  the  electrode  potentials  for 
Cu  |  ^CuS04  and  Zn  |  ^ZnSO4. 

If  time  permits,  determine  the  E.M.F.  of  several  of  the 
following  combinations  — 

Zn  |  rcZnS04  |  KC1  |  7iCuS04  |  Cu 
Zn  |      ZnS04  |  KC1  |      CuS04  |  Cu 


Zn  |  7iZnS04  |  KC1  |      CuS04  |  Cu 


Zn  |      ZnS04  |  KC1  |  7iCuS04  |  Cu 

In  each  case  check  the  results  by  comparing  them  with  the 
algebraic  sum  of  the  electrode  potentials  determined  in  the 
previous  experiments. 

We  have  seen  that  for  a  single  electrode  or  half-element  the 
difference  of  potential  between  the  metal  and  the  solution 
can  be  represented  by  the  equation  — 

0-058.         P 


where  P  is  the  solution  pressure  of  the  metal,  and  p  the 
osmotic  pressure  of  the  metal  ions  in  solution. 

If  Ex  is  the  E.M.F.  of  one  electrode  and  E2  the  E.M.F.  of 
another  electrode,  then  the  E.M.F.  of  the  combination  will  be  — 

P  ?,), 

810j?1         )10^2/' 

where  Ex  and  E2  have  their  correct  sign. 

Influence  of  Change  of  Concentration  of  Salt  Solution  on 
the  E.M.F.  of  a  Cell  —  In  the  above  equation  Cx  can  be  substi- 
tuted for  Px  where  Ct  represents  an  ionic  concentration, 
which  would  just  balance  the  solution  pressure  P,,  similarly 
C2  for  P2. 

For  j9j  and  p2  the  corresponding  ionic  concentrations  may 
be  substituted. 

Hence  the  equation  may  be  written  — 

0-058  C  C 


INFLUENCE  OF  CONCENTRATION  ON  E.M.F.   127 

It  is  obvious  that  the  influence  of  dilution  on  any  given 
electrode  will  depend  upon  whether  ions  are  going  into  the 
solution  from  the  metal,  or  being  deposited  on  it  from  the  solu- 
tion. In  the  former  case  dilution  would  increase  the  E.M.F. 
of  the  electrode  ;  more  ions  would  tend  to  pass  into  solution. 
In  the  latter  case  dilution  would  diminish  the  E.M.F.  of  the 
electrode,  as  the  tendency  to  deposit  ions  on  the  metal  would 
be  reduced. 

If  the  metal  is  the  same  in  both  the  electrodes  —  i.e.,  the 
only  difference  between  them  being  the  concentration  of  the 
salt  solution  —  then  the  solution  pressure  will  be  the  same  on 
both  sides—  e.g.,  P1  and  P2,  therefore  C^Cjj,  hence  the  equa- 
tion simplifies  to  — 


If  we  consider  a  single  half-element,  then  say— 
0-058 


where  Eg  is  the  electrode  potential  for  ionic  concentration  c2, 
and  E!  for  ionic  concentration  cr  If  ^  =  1,  the  equation 
becomes  — 

0-058  . 


Hence,  if  the  concentration  be  increased  or  decreased  ten  times, 
the  potential  difference  will  change  by  -      -  volts. 

71 

Let  Oj  and  a2  be  the  degrees  of  ionization  at  concentration, 
xl  and  x2  of  total   concentration   of  salt,  then  cl  =  alxl  and 


Given  that  a  for  wCuSO4  =  0-21,  and  for  —  CuS04  =  0-385 

using  these  values  for   a,  compare   the   above   theory  with 
results  obtained  in  the  previous  experiment  for  Cu  |  nCuS04, 

and  Cu  |  —  CuS04,  assuming  one  of  them. 

Experiment  to  Determine  the  Electrode  Potential  between  Silver 
and  Silver  Nitrate  Solutions,  at  Concentrations  n  and  -^-  —  Two 
silver  electrodes  are  made  in  a  manner  similar  to  that  de- 


128      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

scribed  for  zinc  and  copper.  In  this  case  the  electrode  must 
be  coated  with  a  fine  deposit  of  silver  by  electrolysis,  in  a 
manner  similar  to  copper  (using  AgN03  and  HN03  instead  of 
CuS04  and  HaS04).  The  electrodes  must  be  tested  as  before. 
Fill  one  tube  with  normal  silver  nitrate  solution,  and  the 

other  with  ~   silver  nitrate  solution.     Combine  them  inde- 

pendently with  a  calomel  electrode  by  means  of  an  indifferent 
electrolyte,  such  as  normal  potassium  nitrate.  Then  measure 
the  E.M.F.  of  each  cell,  as  previously  described. 

Given  that  a  for  normal  silver  nitrate  is   0*58,  and  for 

,-Q  0§81,  and  using  the  value  for  the  normal  silver  nitrate 
electrode  for  E2  in  the  equation  — 

0-058  c 


Calculate  what  the  value  for  Ex  ought  to  be,  and  compare  it 
with  the  experimental  result  (see  next  experiment). 

Experiment  :  Determination  of  E.M.F.  of  a  Cell  in  which  the 
Two  Silver  Electrodes  differ  only  in  Concentration  of  Silver  Nitrate 
Solution  —  Combine  the  two  silver  electrodes  prepared  as 
previously  directed,  giving  the  combination  — 


Ag  |  7iAgN03  |  7iKN03  |      AgN03  |  Ag. 

Determine  the  E.M.F.  as  previously  described.  It  will  be 
observed  that  silver  is  deposited  from  the  more  concentrated 
solution,  while  the  silver  dissolves  in  the  weaker  solution  —  i.e., 
the  concentrations  of  the  two  solutions  tend  to  equalize.  When 
this  point  is  reached,  no  current  passes. 


a  for  %AgN03  =  0-58  ;  a  for       AgN03=  -81. 

Then- 

Co      0-58 

q  =  0^081  =  7'17^=  1  m  equation. 

_,     0-058  . 
-.E=—  log  10  7-17. 

.-.  E  =  0-049  volt. 

The  experimental  result  should  be  within  2  millivolts  of 
this  value. 


CONTACT  POTENTIAL  129 

When  we  have  a  cell  in  which  the  electrodes  only  differ  in 
the  concentration  of  the  salt  solution,  the  cell  is  termed  a 
concentration  cell.  Such  a  cell  is  the  one  used  in  the  last 
experiment. 

Up  to  the  present  we  have  assumed  that  the  contact  poten- 
tial of  the  two  liquids  has  been  illuminated,  but  in  cells  of  this 
type  the  contact  potential  must  be  considered,  since  in  some 
cases  the  contact  E.M.F.  may  be  quite  an  appreciable  fraction 
of  the  total  E.M.F. 

It  can  be  shown  that  the  contact  difference  of  potential 
between  two  solutions  is  due  to  the  different  velocities  of  the 
two  ions,  and  the  dilute  solution  takes  the  potential,  corre- 
sponding with  that  of  the  more  rapid  ions. 

The  contact  potential  between  two  solutions  of  same  electro- 
lyte will  be  — 

_     u-v     0-058  .         c, 


Hence,  taking  all  the  junctions  in  order  — 
C      u-v.         e 


Now,  since  Cx  =  C2  — 

^     0-058  ru-v  .          c,     u  +  v  c2~| 

E  =  —  lm  lQg  10  ^^-v  log  10  -J  J 

c.-} 
^  J 


0-058F     u  +  v  c.     u-v 


10  ^        r        10 
0-058       2v 


n 
2  x  0-058 


-  represents  the  transport  number  of  the  anion,  and  c2  and 

ci  are  the  ionic  concentrations  of  the  metal  ions  in  the  two 
solutions. 

We  have  already  seen  (p.  127)  that  if  we  know  the  ionic 
concentrations  of  the  metal  ions  in  the  two  electrodes  we  can 
calculate  E.  Hence,  if  we  determine  E  experimentally,  and 
then,  using  the  above  equation,  if  we  know  also  the  transport 


130      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

number  of  the  anion  and  the  ionic  concentrations  of  one  of 
the  solutions,  we  can  calculate  the  ionic  concentration  of  the 
other  solution. 

Experiment  to  Determine  the  Concentration  of  Silver  Ions  in 

-TQQ  Solution  of  Silver  Nitrate — Prepare  cell  Ag  |  ^  AgNO3  | 

KN03  |  T^Q  AgN03  |  Ag,  and  determine  E.M.F.  as  before. 

The  transport  number  for  the  anion  is  0-53,  and  the  degree 
of  ionization  for  y^  AgN03  is  0-81. 

.-.  E  =  0-53  x  2  x  0-058  log  10 

E  is  determined  experimentally,  hence  x  can  be  calculated. 
The  degree  of  ionization  for  j-r^r  AgN03  will  be  lOOz,  x  the 

ionic  concentration. 

The  correct  value  for  x  is  0-0093,  but  the  above  concentra- 
tions do  not  rigidly  obey  the  gas  and  dilution  laws,  hence  the 
experimental  value  of  x  is  not  quite  correct.  An  error  up  to 
10  per  cent,  is  allowable. 

Experiment :  Determination  of  the  Solubility  of  Silver  Chloride 
in  Water  by  E.M.F.  Measurements — The  previous  experiment 
shows  that  the  degree  of  ionization  of  a  salt  can  be  easily 
determined  from  the  E.M.F.  measurements.  In  the  case  of 
electrode  Ag  |  AgCl  the  ionic  concentration  of  the  silver 
chloride  solution  is  very  small,  hence  its  conductivity  will  be 
low ;  in  such  a  case  another  more  suitable  soluble  electrolyte  is 

added,  usually  with  a  common  ion.     In  this  case  y^  KC1  is 

very  suitable,  by  this  means  the  conductivity  is  increased  and 
the  results  rendered  more  accurate. 
Prepare  cell — 

AgCl 
roKCl 

7? 

Electrode  Ag  |  AgCl  y~  KC1  is  prepared  by  first  adding  the 
YQ  KC1,  and  then  adding  two  drops  of  silver  nitrate  to  give 


I  looo  AsN°3 1  KN°3 


GAS  CELLS  131 

a  precipitate  of  silver  chloride,  thereby  giving  as  a  saturated 
solution  of  AgCl  in  KC1  solution. 

Determine  the  E.M.F.  as  before, 
then  we  have — 

E  =  0-53x2x0-058  log  - 

—  i.e.,  assuming  ionization  is  complete — i.e.,  a=l.  Hence  x, 
the  ionic  concentration  of  Ag  in  the  AgCl  ^  KC1  |  Ag, 

corresponds  to  the  solubility  of  silver  chloride,  since  silver 
chloride  is  completely  ionized. 

Again,  the  concentration  of  the  chloride  ions  and  silver  ions 
must  be  equal — i.e.  =  x. 

.  \  solubility  product  =  x2  =  K. 

Hence  JK  =  x  is  the  solubility  of  silver  chloride  in  the 
solution.  The  value  is  1-15  x  10  ~5  gram  equivalents  per 
litre. 

Gas  Cells — So  far  we  have  been  concerned  with  cells  in 
which  we  had  soluble  reversible  electrodes.  Insoluble  elect- 
trod  es,  which  do  not  give  rise  to  metallic  ions,  such  as 
platinum,  can  be  prepared.  By  coating  the  platinum  with 
finely  divided  platinum,  it  acquires  the  power  of  absorbing 
gases.  If  such  an  electrode  is  immersed  in  an  electrolytic 
solution,  say  HC1  solution,  and  say  hydrogen  bubbled  through, 
a  certain  amount  of  hydrogen  is  absorbed  by  the  platinum, 
and  a  difference  of  potential  will  be  established  between  the 
solution  and  the  metal.  The  electrode  in  this  case  behaves 
like  a  sheet  of  metallic  hydrogen.  If  positive  electricity 
passes  through  the  solution,  hydrogen  ions  are  discharged 

2H* >H2,  if  negative,  the  gaseous  hydrogen  becomes 

ionized  H2  — ^2H'. 

An  electrode  of  the  above  type  is  known  as  a  hydrogen 
electrode.  An  oxygen  electrode  behaves  similarly. 

Preparation  of  Hydrogen  Electrode — The  glass  portion  of 
the  apparatus  is  very  similar  to  that  used  for  the  calomel 
electrode.  A  convenient  form  is  as  shown  in  Fig.  66. 

It  consists  essentially  of  a  fairly  wide  glass  tube,  A,  with  a 
tube,  suitably  bent,  sealed  into  the  bottom.  This  is  the 
inlet  tube  for  the  gas.  The  electrode  consists  of  a  piece  of 
platinum  foil  2x1-5  cms.,  to  which  is  welded  a  piece  of 


132      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 


platinum  wire,  and  this  in  turn  is  sealed  into  a  glass  tube. 
The  electrode  is  held  in  position  by  means  of  a  rubber 
stopper.  Connection  with  a  second  electrode  is  made  by 
means  of  a  side  tube,  (7.  The  gas  escapes  through  side  tube  D, 
which  is  provided  also  with  an  air  trap,  F. 

The  electrode  must  be  coated  with  an  even  layer  of 
platinum  black.  This  is  best  done  as  described  on  p.  106, 
the  electrode  being  previously  cleaned  with  hot  potassium 
bichromate  and  dilute  sulphuric  acid.  For  efficiency  of  the 


B 


FIG. 


FIG.  67 


electrodes,  the  coating  of  platinum  black  should  be  quite 
uniform  and  fairly  thick,  since  the  amount  of  gas  absorbed 
will  depend  upon  the  thickness  of  the  coating.  The  occluded 
impurities,  chiefly  chlorine,  may  be  removed  by  immersing 
the  electrode  in  an  acidified  (H2S04)  solution  of  a  mixture  of 
ferrous  and  ferric  sulphate  for  about  twenty  minutes.  Then 
thoroughly  wash  the  electrodes  with  distilled  water.  If  not 
required  for  use  immediately,  preserve  it  in  distilled  water. 
Another  form  of  electrode  is  as  indicated  in  Fig.  67.  It 


PREPARATION  OF  HYDROGEN  ELECTRODE        133 

consists  of  a  hard  glass  tube,  A,  sealed  on  to  a  narrow  tube,  B- 
A  short  piece  of  thin  platinum  wire  is  sealed  into  A  at  C. 
The  tube  is  thoroughly  cleaned,  and  then  bulb  A  coated  with 
an  even  layer  of  "liquid  platinum"  (see  Appendix).  The 
tube  is  then  carefully  warmed.  Raise  the  heating  slowly  as 
the  film  drys  and  darkens,  becoming  almost  black.  Then 
heat  the  tube  to  dull  redness,  taking  care  not  to  let  the  tube 
soften.  The  tube  should,  on  cooling,  be  coated  with  a  fine 
grey  metallic  film  of  platinum.  The  wire  C  makes  a  contact 
with  this  film,  so  by  means  of  a  little  mercury  poured  into 
the  tube  a  contact  can  be  made  between  the  film  and  the  rest 
of  the  apparatus. 

The  first  form  of  electrode  has  the  disadvantage  that  it 
requires  several  hours  for  the  gas  in  the  electrode  and  solu- 
tion to  attain  equilibrium,  and  hence  a  constant  potential. 
The  second  type  gives  a  constant  potential  much  quicker,  but 
on  the  whole  is  not  so  efficient  and  reliable  as  the  type  in 
which  rectangular  sheets  of  platinum  are  used. 

Experiment  :  Determination  of  Electrode  Potential  of  tlie  Hydro- 
yen  and  Normal  Hydrochloric  Acid  Electrode  —  Prepare  a  normal 
solution  of  pure  hydrochloric  acid,  and  fill  up  the  electrode  to 
just  about  the  side  tube  C.  Fix  the  platinum  electrode  so  that 
just  over  half  of  it  is  immersed.  The  trap  F  should  contain 
a  little  mercury.  Open  tap  C  (which  need  not  be  lubricated 
with  vaseline)  and  pass  in  a  slow  current  of  hydrogen,  which  has 
been  made  to  pass  through  potassium  permanganate  solution, 
and  then  through  silver  nitrate  solution,  and  finally  through 
normal  hydrochloric  acid  solution,  before  entering  the  elec- 
trode. Close  exit  F,  thereby  forcing  some  of  the  acid  through 
C,  filling  the  tube  ;  then  close  tap  C,  at  the  same  time  opening 
F.  Now  allow  the  hydrogen  to  bubble  through  for  at  least 
an  hour  (longer  if  possible)  to  completely  saturate  the  elec- 
trode with  hydrogen.  Now  complete  the  cell  — 


H2  |  ?*HC1  I  wHCl  |  Hg2Cl27iKCl  |  Hg. 

—  i.e.,  join  up  with  a  calomel  electrode  by  means  of  normal 
hydrochloric  acid.  The  tap  C  should  be  kept  closed,  since  if 
the  barrel  is  wetted  with  the  solution  it  will  be  a  sufficiently 
good  conductor.  The  hydrogen  should  bubble  through  only 
very  slowly.  Now  determine  the  E.M.F.  of  the  cell  by 
balancing  it  against  a  Weston  cell,  exactly  as  in  previous 


134      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

experiments.  In  this  case  it  is  necessary  to  determine  the 
E.M.F.,  say,  every  fifteen  minutes,  until  the  consecutive  read- 
ings practically  coincide. 

Then,  knowing  the  E.M.F.  of  the  cell  and  the  electrode 
potential  for  the  calomel  electrode,  the  electrode  potential  for 
electrode  can  be  calculated  as  in  previous  experiments. 

An  electrode  such  as  the  above,  in  which  the  hydrogen  is 
at  atmospheric  pressure,  and  normal  acid  used,  is  sometimes 
taken  as  the  standard  of  potential  difference. 

The  E.M.F.  is  0-277  volt. 

Experiment  to  Determine  E.M.F.  of  a  Hydrogen  Concentration 
Cell  —  Prepare  cell  — 


H2  |  wHCl  |  nHCl  |        HC1  |  H'. 

Take  the  same  precautions  with  each  electrode  as  described 
in  previous  experiment  for  the  hydrogen  electrode.  Deter- 
mine the  E.M.F.  every  fifteen  minutes,  until  the  E.M.F.  is 
constant. 

The  E.M.F.  in  this  case  is  small,  so  put  the  cell  in  series 
with  the  Weston  cell.  Having  determined  the  E.M.F.  of  the 
cell,  determine  the  degree  of  ionization  of  hydrochloric  acid 

in  normal  solution,  given  that  -  —=0*17  and  the  degree  of 
ionization  for  ,—  ~  hydrochloric  acid  is  0*91. 


Extension  —  In  a  similar  manner  the  student  might  deter 
mine  the  E.M.F.  of— 


H-  |  ?iHCl  |  TiHCl  |  nHCl  |  Cl' 
—  i.e.,  hydrogen-chlorine  cell. 

Electrical  Potentials  of  Oxidation  and  Reduction  Media  — 
When  an  indifferent  electrode,  such  as  platinum  or  iridium,  is 
placed  in  an  oxidizing  solution,  it  will  acquire  a  positive  charge 
relative  to  the  solution  ;  and  if  placed  in  a  reducing  solution,  it 
will  acquire  a  negative  charge. 

If  a  change  from  a  higher  to  a  lower  state  of  oxidation 
occurs,  then  a  positive  charge  is  given  up  or  negative  charge 


OXIDATION  AND  REDUCTION  POTENTIALS          135 

taken  up.  Hence  change  of  ferric  ion  to  ferrous  ion  may  be 
represented  thus— 

Fe  •  •  •  -  (  +  ive  charge)  =  Fe  •  *  ; 
or 

Fe  •"  +  (-  ive  charge)  =  Fe  *  '. 

Reducing  agents  act  in  the  reverse  way.  When  an  oxidizing 
salt  is  present  in  aqueous  solution,  its  affinity  for  a  negative 
charge  will  tend  to  take  such  a  charge  from  the  hydroxyl  ions, 
thereby  liberating  oxygen.  For  example,  if  cobaltic  sulphate 
is  dissolved  in  water  and  sulphuric  acid  added,  the  affinity  is 
sufficient  to  cause  the  liberation  of  oxygen. 

Co2(S04)3  +  H20  =  2CoS04  +  H2S04  +  O  ; 
or 

2Co  •  •  •  +  20H'  =  2Co  •  •  +  H20  +  O. 

Consider  a  cell  made  up  of  a  hydrogen  electrode  on  one  side 
and  a  platinized  electrode  dipping  in  a  solution  of  a  ferrous 
and  ferric  salt  on  the  other,  connected  up  with  some  indifferent 
electrolyte.  When  these  electrodes  are  joined  together,  the 
current  goes  from  the  hydrogen  electrode  to  the  other  in  the 
cell.  Hence  the  hydrogen  is  going  into  solution  —  i.e.,  acquir- 
ing a  positive  charge  —  hence  at  the  other  electrode  the  ion  is 
losing  corresponding  charge.  The  total  change  will  be  — 


—  i.e.,  the  ion  is  reduced.  When  the  cell  is  reversed,  Fe  •  •  will 
be  converted  in  Fe  *  *  *,  and  hydrogen  will  be  liberated.  If,  on 
the  other  hand,  the  platinum  electrode  dips  into  a  solution  of 
stannous  chloride  in  potassium  hydroxide,  and  connected  with 
a  hydrogen  electrode  so  as  to  form  a  cell,  the  current  passes 
from  the  solution  to  the  hydrogen  electrode  in  the  cell  —  i.e., 
hydrogen  ions  are  discharged,  and  the  stannous  ion  acquires 
two  positive  charges,  becoming  stannic. 


In  the  first  case  the  solution  is  said  to  have  an  oxidation 
potential,  and  in  the  second  case  a  reduction  potential. 

Measurement  of  Oxidation  Potentials  :  Experimental  Determina- 
tion of  Electrode  Potential  of  Ferric-Ferrous  Salt  Electrode  —  Both 
oxidation  and  reduction  potentials  are  measured  in  a  precisely 


136      MEASUREMENTS  OF  ELECTROMOTIVE  FORCE 

similar  manner  as  that  used  for  the  measurement  of  single 
potential  differences  between  metals  and  salt  solutions. 

Prepare  a  solution  containing  0-09  gram  molecule 
FeCl3-i-0-01  gram  molecule  FeCl2  per  litre.  Prepare  also 
a  platinized  platinum  electrode  as  directed  for  hydrogen 
electrode.  Fit  up  an  electrode  similar  to  the  metal  salt 
solution  electrode  previously  described — i.e.,  platinum  elec- 
trode immersed  in  the  iron  salt  solution.  Complete  the  cell 
by  combining  it  with  a  normal  hydrogen  electrode  H2  |  wKCl 
by  means  of  an  electrolyte  such  as  normal  KC1.  The  E.M.F. 
of  this  cell  is  then  determined  in  exactly  the  same  manner  as 
in  previous  experiments  (see  Fig.  62).  Then,  taking  the 
hydrogen  electrode  potential  as  0'277  volt,  the  oxidation 
potential  can  be  determined. 

The  result  should  be  about  0-43  volt. 

Further  experiments  may  be  done  in  a  similar  manner  with 
the  following  oxidation  media  : 

0-01  Mol  FeCl3  0-09  Mol  FeCl2  ...  0-32  volt. 

0-1  normal  HMn04       1  '18  volts 

HN03,  6  per  cent 0-67  volt 

HN03,  35  per  cent 075     „ 

HN03,  90  per  cent 0'82     „ 

Measurement  of  Reduction  Potentials — These  measurements  are 
carried  out  in  precisely  the  same  manner  as  in  the  above 
experiments. 

Experiments — Measure  the  reduction  potentials  with  the 
following  media : 

Normal  Cu2Cl2  in  concentrated  HC1 ; 
SnCl2  in  5nHCl. 


CHAPTER  XVI 
VELOCITY  OF  CHEMICAL  REACTION 

ALL  chemical  reactions  require  time  for  their  accomplishment. 
The  actual  velocity  of  the  reaction  is  governed  mainly  by 
Guldberg  and  Waage's  law  of  mass  action,  according  to  which 
the  velocity  of  reaction  at  any  moment  is  proportional  to  the 
concentrations  of  the  substances  taking  part  in  the  reaction. 
Consider  a  simple  reversible  reaction,  such  as  ester  formation, 
in  which  a,  b,  c,  d  are  the  initial  equivalent  concentrations  of 
the  reacting  substances.  Let  x  be  the  amount  of  ester  formed 
in  the  time  t,  the  equation  for  the  velocity  of  reaction  at  any 
instant  will  be  — 

^  =  K(a  -  x)  (b  -  x)  -  K,(c  +  x)  (d  +  x), 

where  dx  is  the  increase  in  the  amount  of  x  during  the  small 
interval  of  time,  dt.  In  many  cases  it  will  happen  that  the 
reaction  is  reversible  only  to  a  very  slight  extent,  and  Kt 
becomes  negligible  in  comparison  with  K.  When  such  is  the 
case,  the  equation  simplifies  down  to  — 


The  simplest  type  of  chemical  reaction  is  that  in  which  only 
one  substance  is  undergoing  change,  and  there  is  practically 
no  back  reaction.  A  reaction  in  which  only  one  molecule  of  a 
single  substance  is  undergoing  change*  is  termed  unimolecular 
reaction,  or  a  reaction  of  the  first  order. 

Unimolecular  Reactions  —  In  cases  where  the  reaction  is 
unimolecular,  the  equation  becomes  — 


137 


138  VELOCITY  OF  CHEMICAL  REACTION 

which  on  integration  gives  — 


2-302 


j-log^-log^a    *)J_ 


Hydrolysis  of  Methyl  Acetate  in  Presence  of  Hydrochloric 
Acid — When  methyl  acetate  is  acted  upon  by  water,  it  is  par- 
tially converted  into  methyl  alcohol  and  acetic  acid.  When 
the  amount  of  water  is  relatively  large,  the  hydrolysis  is  practi- 
cally complete — that  is  to  say,  the  following  equation  goes  from 
left  to  right — 

CH3COOCH3  +  H20  < >  CH3COOH  +  CH3OH. 

The  rate  of  hydrolysis  is  greatly  accelerated  by  the  presence 
of  acids,  and  is,  in  fact,  proportional  to  the  concentration  of  the 
hydrogen  ion. 

Experiment — Prepare  a  standard  solution  baryta,  approxi- 

M 

mately  — ,  and  determine  its  actual  value  by  titration  against 
20 

pure  succinic  acid,  using  phenolphthalein  as  an  indicator. 
Make  up  also  a  semi-normal  solution  of  hydrochloric  acid, 
standardizing  it  by  means  of  baryta  solution  (the  water  used 
should  be  free  from  C02).  Clean  two  small  Erlenmeyer  flasks 
with  steam,  and  dry  them.  Fit  them  with  corks  which  have 
been  previously  soaked  in  paraffin.  It  is  also  necessary  to 
weight  the  flasks  with  a  ring  of  lead,  in  order  to  make  them 
sink  to  a  convenient  depth  in  the  water  of  the  thermostat. 
Two  other  Erlenmeyer  flasks,  about  100  c.c.  capacity,  fitted 
with  corks,  will  be  required  in  which  to  carry  out  the  titra- 
tions;  also  three  pipettes,  one  delivering  20  c.c.  and  two 
delivering  2  c.c.,  also  a  small  stoppered  bottle  containing  pure 
methyl  acetate.  Into  one  of  the  small  Erlenmeyer  flasks 

introduce  20  c.c.  of  —  HC1,  and  into  the  other  40  c.c.   of 

6  HC1.     Suspend  the  flasks  in  a  thermostat  at  25°,  so  that 

z 

they  are  immersed  up  to  the  neck,  also  suspend  the  bottle 
containing  the  methyl  acetate  in  the  thermostat. 

When  the  liquids  have  assumed  the  temperature  of  the 
bath  (i.e.,  about  fifteen  minutes),  introduce  2  c.c.  of  methyl 


HYDROLYSIS  OF  METHYL  ACETATE  139 

acetate  into  one  of  the  flasks  of  acid,  shake  well,  and  at  once 
remove  2  c.c.  of  the  mixture.  This  is  run  into  about  50  c.c. 
of  ice-cold  water,  free  from  CO2,  in  order  to  arrest  the 
reaction,  it  is  then  titrated  as  quickly  as  possible  with  baryta 
solution.  The  moment  when  the  mixture  was  diluted  must 
be  noted.  In  this  way  the  initial  concentration  of  the  acid  is 
determined.  Now  introduce  2  c.c.  of  methyl  acetate  into  the 
other  flask  of  acid,  and  find  the  concentration  of  the  acid  in 
this  case  exactly  as  before,  taking  care  to  note  the  time  when 
the  reaction  is  arrested. 

About  ten  minutes  after  the  first  titration,  again  withdraw 
2  c.c.  of  the  mixture  from  each  of  the  flasks,  and  determine, 
as  before,  the  concentration  of  the  acid,  noting  carefully 
in  each  case  the  moment  when  the  reaction  is  arrested.  Go 
through  the  same  procedure  after  intervals  of  20,  30,  40,  60, 
120  minutes  from  the  starting-point,  and  then,  after  forty-eight 
hours,  carry  out  the  final  titration.  Now,  if  the  initial  titration 
is  To,  and  the  final  titration  Toe,  then  a  is  proportional  to 
Too  —To,  anda  —  x  is  proportional  to  TX-TH,  where  TH  is 
the  titration  after  n  minutes  ;  hence  we  get  — 


K  =  2-302 


Thus  to  calculate  K  it  is  not  necessary  to  calculate  the  actual 
amount  of  ester  hydrolyzed,  but  the  value  of  K  can  be 
obtained  directly  from  the  titration  readings. 

The  velocity  constant  can  be  calculated  from  any  stage  in 
the  reaction.  For  example,  if  Tx  and  TtJ  are  the  titrations  at  the 
times  tx  and  ttj,  then  we  have  — 

K=  2-302 


The  above  experiment  should  now  be  repeated,  using  semi- 
normal  H2S04. 

Assuming  that  the  velocity  constants  are  directly  propor- 
tional to  the  degree  of  ionization  of  the  respective  acids,  calcu- 
late the  degree  of  ionization  of  H2S04  in  semi-normal  solution 
given  — 


The  value  of  a  for  ^  H.2S04  is  0-53. 


140  VELOCITY  OF  CHEMICAL  REACTION 

Exercise — Plot  the  values  of  x  against  the  corresponding 
values  of  time,  and  draw  a  smooth  curve. 

Velocity  of  Inversion  of  Cane  Sugar — Another  very  interest- 
ing reaction  of  the  first  order  is  the  hydrolysis  of  cane  sugar 
into  dextrose  and  laevulose.  This  is  represented  by  the 
equation — 

C12H2aOn  +  H20  =  C6H1206  +  C6H1206. 

As  the  acid  which  accelerates  the  hydrolysis  remains  un- 
altered at  the  end  of  the  reaction,  it  does  not  occur  in  the 
equation.  The  reaction  can  be  conveniently  followed  by 
measuring  the  change  in  the  rotation  of  the  plane  of  polarized 
light.  Whereas  cane  sugar  is  dextro-rotary,  invert  sugar  is 
laevo-rotary,  so  that  the  result  of  inversion  is  that  the  sign  of 
rotation  changes  from  right  to  left. 

As  both  sugar  and  water  take  part  in  the  reaction,  the 
velocity  equation,  according  to  the  law  of  mass  action,  is — 

dx 

dt 


-T7=K.C,sugar  -C Water- 


Since,  however,  the  water  is  present  in  great  excess,  its  con- 
centration, and  therefore  its  active  mass,  remain  practically 
constant  throughout  the  reaction,  and  the  equation  therefore 
reduces  to  one  of  the  first  order. 

The  amount  of  cane  sugar  present  at  any  time  is  propor- 
tional to  the  difference  between  the  angle  of  rotation  at  that 
time  and  the  angle  of  rotation  at  the  end  of  the  reaction. 

If  A0  represents  the  initial  angle,  and  Aoo  the  final  angle 
of  rotation  after  complete  inversion  has  occurred,  and  An  the 
angle  of  rotation  after  time  tn,  then  the  initial  amount  of  cane 
sugar  will  be  proportional  to  A0-Aoo  —  i.e.,  total  change  in 
rotation—  and  An  —  A^  the  amount  of  cane  sugar  present  after 
time  tn  —  i.e.  — 

&  =  A0  —  AOO  and  (a  —  x)  =  An  —  AC*. 

.-.  K  =  2-302 


If  K  is  calculated  for  any  two  readings,  say  tx  ty,  the  equa- 
tion becomes  — 


K  =  o.30o 


-^00)-  log 


)"] 

J 


VELOCITY  OF  INVERSION  OF  CANE  SUGAR        141 

The  values  of  the  angles  must  be  given  their  correct  sign, 
rotations  to  the  right  being  + ,  and  those  to  the  left  - . 

Experiment — Prepare  a  solution  of  cane  sugar  by  dissolving 
20  grams  of  pure  cane  sugar  in  water,  and  making  the  volume 
up  to  100  c.c.  If  the  solution  is  not  clear,  filter  and  add  a 
crystal  of  camphor  as  a  preservative.  Prepare  also  a  normal 
solution  of  hydrochloric  acid. 

Place  30  c.c.  of  the  sugar  solution  and  30  c.c.  of  HC1  solu- 
tion in  separate  flasks,  which  have  been  thoroughly  cleaned 
and  dried,  and  suspend  the  flasks  in  a  thermostat  at  25°  C. 
Set  up  a  polarimeter,  and  place  a  clean,  jacketed,  observation 
tube  in  the  polarimeter.  Circulate  water  at  25°  C.  between 
the  jacket  and  the  observation  tube  (see  Fig.  36),  and  deter- 
mine the  zero  (see  Polarimeter  Measurements). 

Mix  the  acid  and  sugar  solutions  thoroughly,  and,  as  soon 
as  possible,  fill  the  observation  tube  with  the  mixture,  and 
determine  the  angle  of  rotation.  Note  the  time  at  which  the 
reading  is  made. 

The  angle  of  rotation  changes  rather  rapidly  at  first,  so  take 
five  or  six  readings  in  succession,  and  note  the  time  for  the 
first  and  last  of  these  readings.  The  mean  value  of  the  angles 
should  be  taken  as  A0  at  the  time,  halfway  between  the  first 
and  last  reading  being  taken  as  the  starting-point  of  the 
reaction.  Take  subsequent  readings  after  10,  20,  40,  60, 
120  minutes,  and  a  final  reading  after  forty-eight  hours,  the 
tube  being  kept  during  this  latter  period  in  a  thermostat. 
Calculate  the  value  of  K  from  the  equation  given. 

The  value  for  a  20  per  cent,  sugar  solution,  with  equal 
volume  of  normal  HQ  at  25°,  is  0*00472. 

The  experiment  should  be  repeated  with  normal  H2SO4. 

Note—  The  value  of  zero  should  be  redetermined  at  the  end 
of  the  experiment,  in  order  to  see  that  it  has  been  constant 
during  the  experiment. 

Bimolecular  Reactions — When  two  substances  react  and 
both  alter  in  concentration,  the  reaction  is  said  to  be  bimolec- 
ular  or  of  the  second  order.  If  the  initial  molecular  concentra- 
tion of  one  substance  is  a,  that  of  the  other  b,  and  x  the  amount 
transformed  in  the  time  t,  the  velocity  equation  is — 

~  =  K(a-x)(b-x). 


142  VELOCITY  OF  CHEMICAL  REACTION 

When  the  substances  are  present  in  equivalent  quantities, 
the  equation  becomes  — 


which  on  integration  gives  — 

K     l       x 

JV  =  -  —  r  -  —  v. 

t  a(a  -  x) 

When  the  reacting  substances  are  not  present  in  equivalent 
proportions,  the  calculation  is  somewhat  more  complicated  on 
integrating  — 

dX          IT-/  v     ,7  x 

-^  =  K(a-x)(b-x) 
we  get  — 


(a-b)t' 
2-302 


^ 
g 


(a  -ft)/       l°  (&-»)« 

Experiment:  Saponification  of  Ethyl  Acetate  with  Sodium 
Hydroxide  —  In  this  case  the  velocity  of  saponification  is 
approximately  proportional  to  the  concentration  of  OH'  ions  — 

CH3COOC2H5  +  OH'  =  CH3COO'  +  C2H5OH. 

This  reaction  differs  from  the  hydrolysis  by  acids,  where 
the  concentration  of  H  ion  remains  unchanged  ;  in  this  case 
the  concentration  of  the  OH'  ion  changes  throughout  the 
experiment. 

7? 

Make  up  -  -   solution  of  ethyl  acetate.     Place  50  c.c.  in  an 

Erlenmeyer  flask  (100  c.c.),  fitted  with  a  paraffin  cork,  and 
suspend  in  a  thermostat  at  25°.  Into  a  similar  flask  intro- 

N 
duce  50  c.c.  of  --  NaOH  (free  from  carbonate),  and  suspend 

this  also  in  the  thermostat.  When  these  two  solutions  have 
acquired  the  temperature  of  the  thermostat,  pour  the  alkali 
into  the  ester,  and  shake  the  mixture  well.  The  initial  alkali 
concentration  is  calculated  from  the  amount  of  alkali  added, 
after  correcting  for  the  amount  of  alkali  which  has  remained 
on  the  sides  of  the  flask;  the  latter  is  found  by  titration. 


BIMOLECULAR  REACTIONS  143 

After  intervals  of  3,  5,  10,  20,  30,  60,  90  minutes,  5  c.c.  of  the 
mixiure  is  withdrawn  and  run  into  a  known  volume  of 

^r  HC1.     The  excess  of  acid  is  found  by  titration  with  baryta. 

The  mean  point  of  the  time  taken  to  introduce  the  5  c.c.  mix- 
ture into  the  acid  is  taken  as  time  at  which  the  reaction  was 
stopped.  The  final  titration  should  be  taken  after  twenty- 
four  hours. 

K  can  then  be  calculated  from  the  following  equation — 

K  =  T?J  P°g  10 Te  +  loglo(T° "  Too)  ~ log  loT° ' log lo(Tf "  T*)]) 
where  TO,  T,,  T^  are  the  numbers  of  cubic  centimetres  of 
acid  required  to  neutralize  the  amount  of  alkali  in  the  mixture 
at  the  beginning  of  the  reaction,  after  the  interval  of  time,  t, 
and  at  the  end  of  the  reaction  respectively.  The  actual  value 
of  K  obtained  depends  on  the  normality  of  the  solutions  when 
it  is  calculated  in  the  manner  indicated  above,  but  the  value 

which  would  be  obtained  with  normal  solutions  can  be  calcu- 

Y 

lated  by  multipling  the  above  expression  by  ^.,  where  V  is  the 

number  of  cubic  centimetres  removed  for  each  titration,  and 
N  the  normality  of  the  standard  acid ;  in  this  case  5  and  ^ 
respectively. 

Determination  of  the  Order  of  a  Reaction — Velocity  measure- 
ments are  made  with  definite  concentrations  of  the  reacting 
substances,  and  with  double  and  treble  those  concentrations, 
determining  in  each  case  the  times  taken  to  complete  a  definite 
fraction  (say  one-third)  of  the  total  change.  Then,  according  to 
Ostwald,  the  order  of  reaction  can  be  determined  as  follows : 

1.  For  a  reaction  of  the  first  order,  the  time  taken  to  com- 
plete a  certain  fraction  of  the  reaction  is  independent  of  the 
initial  concentration. 

2.  For  a  reaction  of  the  second  order,  the  time  taken  to 
complete  a  definite  fraction  of  the  reaction  is  inversely  propor- 
tional to  the  initial  concentration — i.e.,  if  the  concentration  is 
doubled,  the  time  is  halved  to  complete  the  same  fraction  of 
the  reaction. 

3.  Generally  speaking,  for  a  reaction  of  the  wth  order,  the 
times  taken  to  complete  a  certain  fraction  of  the  reaction  are 
inversely   proportional   to   the   (n  —  1)  power   of   the   initial 
concentration. 


CHAPTER  XVII 
QUANTITATIVE  ELECTROLYTIC  ESTIMATIONS 

Quantitative  Electrochemical  Analysis.  Electrolytic  Deter- 
mination of  Metals — There  are  many  advantages  in  favour  of 
electrolytic  methods,  where  available,  over  the  usual  gravimetric 
method.  The  latter  are  frequently  very  laborious,  and  at  the 
same  time  the  chances  of  error  are  not  by  any  means  small. 
The  electrolytic  methods,  on  the  other  hand,  are  usually  very 
much  simpler,  quicker,  and  determination  can  be  made  with  a 
very  high  degree  of  accuracy,  hence  electrolytic  methods  are 
coming  more  and  more  into  use,  particularly  in  the  commercial 
world.  The  metals  are  usually  estimated  in  the  form  of  the 
pure  metal  or  in  the  form  of  a  metallic  oxide.  In  order  to 
make  a  successful  determination  it  is  essential  that  the  metal 
should  be  obtained  as  a  very  fine  deposit  firmly  adhered  to 
the  cathode,  and  as  smooth  as  possible,  so  that  it  can  be  well 
washed  without  any  marked  loss.  If,  on  the  other  hand,  the 
deposit  is  coarse  or  granular,  it  is  very  liable  to  be  lost  in  the 
washing  of  the  deposit,  and  at  the  same  time  is  liable  to  be 
impure.  In  order  to  obtain  a  successful  deposit  the  potential 
difference,  temperature,  and  current  density  must  be  carefully 
controlled. 

Apparatus — The  most  suitable  form  of  apparatus  is  as  shown 
in  Fig.  68.  A  light  platinum  dish,  A,  serves  as  the  cathode, 
and  is  supported  on  a  suitable  stand  by  means  of  a  metal  ring. 
The  anode  B  is  usually  of  the  form  of  a  flat  spiral  of  platinum, 
or  in  some  cases  a  flat  perforated  platinum  plate  welded  to  a 
platinum  wire,  the  object  of  the  perforations  being  to  allow 
the  escape  of  gas  which  would  otherwise  collect  under  the 
plate.  The  other  connections  are  as  shown  in  Fig.  67.  The 
current  and  voltage  are  noted  by  means  of  an  ammeter,  M,  and 
voltmeter,  V,  respectively,  the  voltmeter  being  placed  between 

144 


ELECTROLYTIC  DETERMINATION  OF  METALS      145 

the  anode  and  cathode.  Another  simpler  form  of  apparatus 
is  as  shown  in  Fig.  69,  the  hollow  platinum  cylinder  being 
used  instead  of  a  platinum  dish,  and  the  apparatus  being 
placed  in  a  beaker. 

In  all  experiments  it  is  necessary  to  know  the  cut-rent  density 
at  the  electrodes.  In  the  case  of  metallic  depositions  the 
current  density  at  the  cathode  only  is  required.  The  current 
density  is  usually  expressed  in  amperes  per  square  centi- 
metres, or  amperes  per  100  square  cms.  Hence  the  surface  of 
the  electrode  used  must  be  calculated.  This  may  be  done  once 
for  all  for  a  given  volume  of  liquid  in  the  basin. 


FIG.  68 


FIG.  69 


Experiment :  Electrolytic  Determination  of  Copper — Weigh  out 
accurately  1  gram  of  CuSO45H20  and  dissolve  in  a  little 
water  (distilled)  ;  transfer  to  the  platinum  basin,  adding  the 
washings,  and  make  up  to  a  suitable  volume,  then  add  3  per 
cent,  by  volume  of  nitric  acid.  Heat  the  solution  to  about 
50°  to  60°  C.,  and  keep  the  temperature  approximately  constant 
by  placing  a  small  flame  under  the  basin.  Pass  a  current  of 
E.M.F.  2'2  to  2'5  volts  and  a  current  density  0'5  to  2*5  am- 
peres per  100  square  cms.  The  nitric  acid  becomes  gradually 
weaker  during  electrolysis,  so  from  time  to  time  a  few  more 
drops  should  be  added.  The  dish  should  be  covered  with  a 
10 


146     QUANTITATIVE  ELECTROLYTIC  ESTIMATIONS 

clock-glass,  which  has  a  hole  in  the  centre  for  the  anode  wire 
to  pass  through.  To  test  whether  the  copper  has  been  com- 
pletely deposited,  add  a  few  cubic  centimetres  of  distilled 
water,  thereby  raising  the  level  of  the  liquid  in  the  basin,  and 
note  whether  any  copper  is  deposited  on  the  fresh  surface. 

The  solution  is  tested  finally  by  removing  a  drop  of  the 
liquid  by  means  of  a  glass  rod,  and  touching  a  drop  of 
ammonia  solution  on  a  white  tile.  If  the  deposition  is  incom- 
plete, a  blue  colour  will  result. 

When  the  whole  of  the  copper  has  been  deposited  it  is 
essential  to  remove  the  liquid  before  the  current  is  stopped, 
otherwise  the  nitric  acid  will  redissolve  some  of  the  copper. 
First  dilute  the  solution  with  distilled  water,  then  syphon  off 
the  liquid  by  first  filling  a  bent  glass  tube  with  water,  closing 
one  end  with  the  finger,  and  then  putting  the  other  end  of  the 
tube  below  the  surface  of  the  liquid  in  the  basin,  then,  on 
removing  the  finger,  the  liquid  will  siphon  over.  As  the 
liquid  is  removed  from  the  basin  the  distilled  water  must  be 
added  so  as  to  keep  the  electrodes  wholly  immersed.  This  is 
done  until  the  acid  is  too  dilute  to  affect  the  copper.  The 
current  is  stopped,  the  basin  removed,  and  the  deposit  washed 
once  or  twice  with  distilled  water  and  then  with  alcohol,  and 
finally  dried  in  an  air  oven  at  80°.  The  basin  +  deposit  is 
then  weighed,  and  then,  by  subtracting  the  weight  of  the 
basin,  the  amount  of  copper  can  be  estimated.  Note — the 
deposit  should  be  perfectly  smooth  and  uniform. 

Technical  Application  of  the  Above  Method — A  solution  con- 
taining copper  and  metals  of  the  iron  group  can  be  analyzed 
quantitatively  for  copper  by  the  above  method,  since  the  iron 
group  metals  remain  dissolved  in  the  nitric  acid.  Commercial 
copper  and  many  copper  ores  frequently  contain  as  impurity 
arsenic  and  antimony ;  on  electrolysis  some  of  the  arsenic  and 
antimony  are  deposited  also,  giving  a  brownish  colour  to  the 
copper.  In  this  case  the  deposit  is  dried  and  weighed  as 
before,  and  then  ignited  over  a  bunsen  flame.  The  arsenic 
and  antimony  volatilize,  leaving  the  copper  as  copper  oxide. 
This  is  dissolved  in  dilute  nitric  acid,  and  the  copper  once 
more  deposited,  washed,  dried,  and  weighed  as  before.  The 
difference  in  the  last  two  weighings  gives  the  amount  of 
arsenic  and  antimony  which  had  been  deposited. 

The  above  method  is  frequently  used  to  estimate  copper,  in 
simple  commercial  alloys  such  as  copper-aluminium,  etc. 


ELECTROLYTIC  DETERMINATION  OF  METALS      147 

Electrolytic  Estimation  of  Lead — In  this  case  the  lead  is  not 
estimated  as  metallic  lead,  but  in  the  form  of  peroxide.  The 
deposit  is  formed  at  the  anode,  so  in  this  experiment  the 
basin  is  made  the  anode.  If  possible,  a  basin  with  an 
unpolished  surface  is  preferable,  as  the  deposit  is  not  as  fine 
as  in  the  case  of  copper,  and  the  rough  surface  assists  the 
adherence  of  the  deposit. 

Experiment — Weigh  out  into  the  basin  about  1  gram  of,  say, 
lead  nitrate,  dissolve  in  distilled  water,  add  nitric  acid  until  the 
solution  contains  10  per  cent,  of  free  nitric  acid.  Keep  the  liquid 
at  a  temperature  of  about  55°,  and  electrolyze  with  a  current 
of  E.M.F.  2-3  to  2-7  volts  and  current  density  of  1  to 
2  amperes  per  100  sq.  cms.  Test  the  end-point  first  by  raising 
the  level  of  the  liquid  in  the  basin,  and  finally  by  removing  a 
drop  on  a  watch-glass  and  adding  ammonia  and  ammonium 
sulphide.  Siphon  off  the  liquid  as  before. 

Then  carefully  wash  the  hydrated  oxide  deposit  with  dis- 
tilled water,  and  dry  at  185°  in  an  air  oven  until  the  weight  is 
constant.  From  the  weight  of  peroxide  calculate  the  amount 
of  lead.  The  estimation  usually  requires  one  and  a  half  hours. 
To  clean  the  anode  add  hot  dilute  nitric  acid  and  a  few  crystals 
of  oxalic  acid. 

Electrolytic  Estimation  of  Nickel — In  this  case  the  basin  will 
be  the  cathode.  Dissolve  1*5  grams  of  nickel  ammonium 
sulphate  and  4  grams  of  ammonium  oxalate  in  water  (120  c.c.). 
Electrolyze  with  a  current  density  of  1  ampere  per  100  sq. 
cms.  and  E.M.F  2-5  to  3-5  volts.  Other  details  as  for  copper. 

Theoretical  Explanation  of  Electrolytic  Depositions — We  have 
already  seen  that  the  potential  between  a  metal  and  its  salt  is 
given  by  the  equation—  Q.Q5g  p 

E-— log,.-, 

where  P  is  the  solution  pressure  of  the  metal,  and  p  is  the 
osmotic  pressure  of  the  metallic  ions  in  the  solution.  Now, 
the  potential  difference  between  a  metal  and  its  ions  may  be 
considered  as  a  sort  of  affinity  of  the  metal  for  a  certain 
charge  either  positive  or  negative,  hence  to  convert  metallic 
ions  into  free  metal  we  have  only  to  apply  a  contrary  E.M.F. 
slightly  higher  than  the  potential  difference.  In  this  case  it 
is  termed  the  decomposition  potential,  and  its  value  is  given  by 
the  equation- 


148     QUANTITATIVE  ELECTROLYTIC  ESTIMATIONS 

The  value  of  E  will,  however,  be  slowly  changed  as  the 
metal  is  deposited,  since  the  value  of  p  is  changing ;  but  even 
if  the  concentration  be  diminished  10000  times,  the  change  in 
the  decomposition  is  only  4  x  0'058  =  0-232  volt  for  a  mono- 
valent  element,  and  half  this  for  a  divalent  element,  which  is 
comparatively  small. 

Suppose,  then,  we  have  a  solution  of  two  metals  whose 
decomposition  potentials  are  not  too  near  the  same  value, 
then  it  is  possible  to  separate  the  metals  by  carefully  adjusting 
the  potential  difference  applied  to  the  solution. 

Example  Experiment :  Determination  of  Silver  and  Copper  in 
an  Alloy  of  the  Two  Metals — Dissolve  0-5  gram  of  the  alloy, 
2  c.c.  of  nitric  acid  (1:3)  diluted  with  water ;  make  up 
to  150  c.c.  Add  5  c.c.  of  absolute  alcohol,  and  raise  the 
temperature  to  55°  C.  The  alcohol  and  the  temperature 
prevent  the  formation  of  silver  peroxide  at  the  anode. 

Electrolyze  the  solution  with  a  current  of  E.M.F.  1'36±0'1 
volt  and  current  density  0*5  to  1  '5  amperes  per  100  sq.  cms. 
Great  care  must  be  taken  to  keep  the  voltage  constant. 

When  the  electrolysis  is  complete,  quickly  decant  off  the 
solution  into  a  beaker,  wash  the  silver  with  a  little  water, 
add  washings  to  solution,  wash  with  alcohol,  and  dry  at  80°, 
and  weigh.  Clean  the  basin  and  completely  transfer  the 
solution  into  it,  and  determine  the  copper  under  the  con- 
ditions for  copper — i.e.,  increase  the  potential  to  2'2  to  2'5  volts. 

Quantitative  Estimation  of  Nitric  Acid  (or  Nitrates)  by 
Electrolytic  Reduction  to  Ammonia — Nitric  acid  or  nitrates 
in  the  presence  of  sulphuric  acid  is  reduced  at  the  cathode 
during  electrolysis.  The  product  of  reduction  depends  on  the 
nature  of  the  metal  at  the  electrode.  If  platinum  is  used,  no 
ammonia  is  evolved ;  but  if  a  little  copper  salt  is  added, 
copper  is  deposited  on  the  cathode,  reduction  at  once  com- 
mences, and  the  greater  portion  of  the  nitrate  is  transformed 
in  ammonium  salt. 

The  ionic  equation  is — 

K08'  +  8H-  =  NH3  +  OH'  +  2H2O. 

Under  ordinary  conditions  a  certain  amount  of  hydroxylamine 
is  always  formed. 

N(y  +  6H-  -  NHaOH  +  OH'  +  H20. 
The  relative  proportions  of  ammonia  and  hydroxylamine 


ESTIMATION  OF  NITRATES  149 

depend  on  the  physical  nature  of  the  electrode.  For  example, 
according  to  Tafel,  if  a  smooth  copper  electrode  is  used,  11-5 
parts  of  hydroxylamine  to  76 -8  parts  of  ammonia  are  formed, 
whereas  if  the  electrode  is  coated  with  electro-deposited 
copper,  1  part  of  hydroxylamine  to  92 '3  parts  of  ammonia 
results. 

The  problem  is  to  reduce  the  production  of  hydroxylamine 
to  a  negligible  amount.  A  small  amount  of  hydroxylamine  is 
counter-balanced  by  solution  of  a  small  amount  of  copper 
from  the  electrode  in  the  sulphuric  acid. 

Ulsch  has  succeeded  in  obtaining  conditions  under  which 
nitrates  can  be  estimated  to  within  O'l  per  cent. 

Apparatus — Prepare  a  copper  cathode.  By  winding  about 
2  metres  of  copper  wire  1*4  mm.  diameter  round  a  glass  tube, 
15  mm.  diameter,  so  as  to  give  about  forty 
rounds,  are  formed.  About  15  cms.  of  wire 
are  left  over  and  bent  so  as  to  lie  along  the  axis 
of  the  spiral  cylinder.  Remove  the  glass 
tube  and  draw  out  the  spiral  so  that  each  turn 
is  just  separated  from  the  next,  the  total 
length  of  the  spiral  being  about  70  mm. 

Make  an  anode  of  thin  platinum  wire,  sup- 
porting it  on  a  glass  tube ;  this  passes  down 
the  centre  of  the  copper  spiral  (see  Fig.  70). 
The  liquid  to  be  electrolyzed  is  contained  in  a 
test-tube-like  tube,  2  cms.  diameter,  cms.  long, 
the  two  electrodes  being  held  in  position  by 
means  of  a  cork,  which  must  be  fitted  with  ^IG-  ?° 
an  outlet  for  the  gases  evolved  during  electrolysis. 

Prepare  the  copper  electrode  by  coating  it  with  spongy 
copper  in  a  copper  voltameter  (see  p.  122),  using  current 
density  of  about  3  amperes  per  100  sq.  cms. 

Experiment :  Determine  the  Amount  of  Nitrate  in  a  Sample  of 
Potassium  Nitrate — Dissolve  0'5  of  a  gram  of  potassium  nitrate 
in  a  little  water,  and  add  exactly  50  c.c.  of  normal  sulphuric 
acid.  Make  up  to  100  c.c.  with  water.  Take  20  c.c.  of  this 
solution  and  transfer  it  to  the  glass  cell  and  fit  the  electrodes 
in  position  (they  should  go  right  to  the  bottom).  If  the  spiral 
is  not  covered,  add  a  little  water.  Now  electrolyze  the  solu- 
tion, using  an  E.M.F.  of  4  volts  and  a  current  density  of 
2 '5  to  3  amperes  per  100  sq.  cms.  The  current  density  should 
not  be  above  this,  otherwise  the  amount  of  hydroxylamine 


150     QUANTITATIVE  ELECTROLYTIC  ESTIMATIONS 

becomes  appreciable.  No  gas  will  be  evolved  at  first,  since 
reduction  is  taking  place ;  but  when  the  reduction  is  nearing 
completion,  hydrogen  is  evolved  quite  freely.  When  this 
occurs,  continue  the  electrolysis  for  a  further  period  of  fifteen 
minutes,  to  be  sure  of  complete  reduction.  Remove  the  elec- 
trode carefully  before  breaking  the  current ;  wash  then  with 
distilled  water,  and  keep  the  washing  in  a  beaker.  Then 
transfer  the  contents  of  the  tube  to  the  beaker  containing  the 
washings,  and  wash  out  the  tube.  Then  titrate  the  unused 
acid  with  standard  alkali. 

The  equation  for  the  reaction  is — 

2KN03  +  2H2S04  +  8H2  =  K2S04  +  (NH4)2S04  +  6H20 

— i.e.,  two  equivalents  of  acid  for  one  equivalent  of  nitrate.  From 
the  amount  of  acid  used  (in  this  case  50  c.c.  normal  acid)  the 
amount  of  nitrate  can  be  calculated.  With  careful  manipula- 
tion not  more  than  0-1  to  O2  per  cent,  error  should  be  allowed. 


CHAPTER  XVIII 
ELECTROLYTIC  PREPARATIONS 

Reduction  of  Aromatic  Nitre-Compounds — The  final  pro- 
duct in  the  reduction  of  aromatic  nitre-compounds  is  the 
amine,  but  it  is  possible  to  obtain  a  large  number  of  inter- 
mediate products,  corresponding  to  the  various  stages  of 
reduction,  by  carefully  controlling  the  conditions  of  the  re- 
action. The  whole  process  is  usually  a  combination  of  electro- 
chemical reductions  and  purely  chemical  reactions.  As  an 
example  we  will  consider  nitrobenzene. 

The  following  diagram  represents  all  the  important  changes 
in  the  reduction  of  nitrobenzene  : 

C6H5N02 


i  /o\      j 

*C6H5       C6H5X-NC6H* 

C.HLNHOH 


-  NHC6H5 


64 


OH  (1) 


^NH2  (4) 

Reduction  in  Moderately  Acid  Solutions — The  following 
series  of  products  are  formed  in  which  the  last  is  the  principal 
final  product : 

( 1)  C6H5N02  +  H2  =  H20  +  C6H5NO. 

(2)  CfiH5NO>H2  =  C6H5NHOH. 

(3)  C6H5NHOH  +  H2  =  C6H5NH2  +  H20. 

Reductions  in  Strongly  Acid  Solutions — In  this  case  the 
reduction  stops  at  the  end  of  equation  (2)  above — i.e.,  the 
principal  reduction  product  being  C6H5NHOH. 

151 


152  ELECTROLYTIC  PREPARATIONS 

Under  the  influence  of  the  strong  acid  the  phenyl-hydroxy- 
lamine  is  converted  into  the  isomeric  para-amido  phenol — 


NH2 

Reduction  in  Alkaline  Solution — In  this  case  the  equations 
(1)  and  (2)  are  fulfilled,  and  these  combine  as  follows : 

/o\ 

(4)  C6H6NHOH  +  C6H5NO  =  C6H6N  -  NC6H5  +  H20. 

/0\ 

(5)  C6H6N  -  NC6H5  +  2H2  =  C6H5NH - NHC6H5  +  H20. 


/\ 
3C6H5NH  -  NHC6H5  +  2C6H5N02  =  C6H5N  -  NC6H5  + 


(6) 


Hence  azo-benzene  is  the  principal  final  product.  The  re- 
duction of  hydrazo-benzene  to  aniline  only  takes  place  to  a 
slight  extent. 

Preparation  of  Aniline  from  Nitrobenzene  —  Take  a  tall 
beaker  and  place  inside  a  porous  pot  to  serve  as  the  anode 
chamber,  the  cathode  chamber  being  the  space  between  the 
porous  pot  and  the  walls  of  the  beaker.  The  anode  consists  of 
strips  of  sheet  lead  (about  2  to  3  mm.  thick),  the  cathode  is  also 
of  sheet  lead,  but  it  should  be  perforated.  The  cathode  is 
bent  in  the  form  of  a  cylinder  so  as  to  encircle  the  porous  pot. 
Introduce  into  the  anode  chamber  dilute  sulphuric  acid  of 
specific  gravity  ri.  For  the  cathode  liquor  make  a  mixture 
of  20  grams  of  nitrobenzene,  150  c.c.  of  alcohol,  and  125  c.c. 
of  dilute  sulphuric  acid,  specific  gravity  1*2.  Electrolyze  the 
solution  with  a  current  of  density  4  to  8  amperes  per  100 
sq.  cms.  at  the  cathode,  and  voltage  about  5  volts.  After 
the  passage  of  about  26  ampere  hours,  remove  a  little  of  the 
cathode  liquid  and  titrate  with  sodium  nitrite.  If  the  result 
indicates  about  85  to  89  per  cent,  of  the  theoretical  quantity  of 
aniline,  remove  the  cathode  liquid,  distil  off  the  alcohol,  cool, 
and  about  20  grams  of  aniline  sulphate  should  crystallize  out. 
The  crystals  may  be  decomposed  with  caustic  soda,  and  the 
mixture  steam  distilled. 

The  o.m.p.  toluidines  can  be  similarly  prepared,  but  in  the 


PREPARATION  OF  AZOBENZENE        153 

case  of  the  reduction  of  ^-nitrotoluene  the  percentage  is 
lower. 

Preparation  of  Azobenzene  from  Nitrobenzene  —  In  this 
case  nickel  electrodes  are  used,  otherwise  the  apparatus  is  as 
before.  The  anode  liquid  is  a  cold  saturated  solution  of 
sodium  carbonate,  and  is  contained  in  the  porous  cell.  The 
cathode  liquid  consists  of  20  grams  of  nitrobenzene,  5  grams 
of  crystallized  sodium  acetate  dissolved  in  200  c.c.  of  70  per 
cent,  alcohol.  The  cathode  density  should  be  6  to  9  amperes. 
The  electrolysis  is  carried  out  at  boiling-point,  and  almost 
immediately  after  the  theoretical  amount  of  current  has  been 
passed  (17*5  ampere  hours),  a  considerable  amount  of  hydrogen 
begins  to  come  off;  at  this  point  lower  the  current  density 
and  pass  1  to  2  ampere  hours'  more  current.  The  contents  of 
the  cathode  are  now  free  from  nitrobenzene,  but  contains  a 
small  amount  of  hydrazobenzene  and  azoxybenzene.  The 
bulk  of  the  azobenzene  crystallize  out  almost  chemically 
pure,  and  may  be  filtered  off  on  a  Buchner  funnel.  The  re- 
mainder is  precipitated  by  the  addition  of  water  or  distilled 
off  in  steam,  and  purified  by  re-crystallization  from  alcohol  or 
ether.  The  current  efficiency  is  over  80  per  cent.,  and  the 
yield  is  over  90  per  cent,  of  the  theoretical  amount. 

Preparation  of  lodofonn — When  free  iodine  is  warmed  with 
water  and  an  aqueous  alkaline  solution  of  alcohol,  iodoform  is 
formed  according  to  the  following  equation : 

CH3CH2OH  +  10I2  +  H20  =  CHI3  +  C02  +  7HI. 

The  hydriodic  acid  then  reacts  with  the  alkali  to  form  iodide. 
Iodoform  is  prepared  electrolytically  by  electrolyzing  a  solu- 
tion containing  potassium  iodide,  sodium  carbonate,  and  ethyl 
alcohol.  Free  iodine  is  liberated  at  the  anode,  which  reacts 
with  the  alcohol  yielding  iodoform.  The  purely  chemical 
method  only  gives  a  yield  of  about  40  per  cent.,  whereas  the 
electrolytic  method  gives  as  much  as  98  per  cent,  yield.  The 
anode  consists  of  a  large  sheet  of  platinum  (or  wire  gauze),  the 
cathode,  which  is  relatively  small,  is  made  of  nickel  or  platinum 
foil  wrapped  in  parchment.  The  anode  liquid  consists  of  a 
solution  of  20  grams  of  anhydrous  sodium  carbonate,  20  grams 
of  potassium  iodide,  200  c.c.  of  water,  and  50  c.c.  of  alcohol 
(96  per  cent.).  This  solution  is  poured  into  the  porous  cell ; 
the  cathode  liquor  is  a  solution  of  sodium  carbonate.  The 


154  ELECTROLYTIC  PREPARATIONS 

experiment  is  carried  out  at  50°  to  70°,  with  a  current 
density  at  the  anode  of  1  to  3  amperes  per  100  sq.  cms., 
and  a  cathode  current  density  of  4  to  8  amperes  per  100 
sq.  cms.  During  electrolysis  the  solution  tends  to  become 
alkaline,  so  a  slow  stream  of  carbon  dioxide  must  be  bubbled 
through  the  cathode  liquid  so  as  to  neutralize  the  caustic  soda 
formed.  The  solution  should  be  from  light  to  dark  yellow  ;  if 
it  becomes  brown,  interrupt  the  current  of  carbon  dioxide  for 
a  short  time. 

The  electrolysis  should  be  allowed  to  continue  for  about 
three  hours  in  order  to  get  a  fair  quantity  of  iodoform.  Then 
on  cooling  the  iodoform  separates  out,  and  is  filtered  off, 
washed  with  water,  and  dried  at  room  temperature.  The 
filtrate,  after  the  addition  of  fresh  quantities  of  potassium 
iodide  and  alcohol,  may  be  used  over  again,  until  it  contains 
large  quantities  of  potassium  iodate  and  carbonate.  The  cur- 
rent efficiency  is  80  per  cent.  The  equation  given  above 
represents  the  formation  of  iodoform,  neglecting  the  inter- 
mediate products  and  secondary  reactions.  The  hydriodic 
acid  reacts  with  the  sodium  carbonate  to  give  sodium  iodide 
and  carbonic  acid.  The  sodium  iodide  is  continually  decom- 
posed by  the  current,  thereby  making  fresh  quantities  of 
iodine  available  at  the  anode.  The  iodine  produced  at  the 
anode,  coming  in  contact  with  free  alkali  or  alkali  carbonate 
from  the  cathode,  forms  hypoiodite,  both  as  alkali  salt  and  as 
free  acid  ;  this  reacts  with  the  alcohol  by  simultaneous  oxida- 
tion and  iodizing,  to  produce  iodoform  and  carbonic  acid.  The 
chief  by-product  is  alkali  iodate,  which  is  produced  from  that 
portion  of  the  iodide  which  does  not  immediately  react  with 
the  alcohol. 


(1)  2HI  +  Na2C03=2NaI 

(2)  2NaI  +  2H20  =  2NaO 

(3)  I2  +  2NaOH  =  NaI  +  NaIO  +  H2O. 

(4)  M  alO  +  ILO^—  r>  NaOH  +  HIO. 

(5)  5HIO  +  C2H5OH  =  C02  +  CHL  +  2HI  +  4H20. 

(6)  3HIO=2HI  +  HI03. 
(7) 


It  is  not  possible  to  prepare  the  corresponding  bromoform 
and  chloroform  by  a  similar  method,  as  aldehydes  and  other 
products  of  oxydation  of  alcohol  are  given  on  electrolysis. 
This  is  due  to  the  fact  that  the  decomposition  potential  of 


PREPARATION  OF  AMMONIUM  PERSULPHATE      155 

iodine  from  potassium  iodide  and  soda  solution  is  only  1*12 
(normal  hydrogen  electrode  as  zero),  whilst  oxygen  is  liberated 
at  1-7.  With  potassium  bromide  alcohol  and  sodium  car- 
bonate, bromide  separates  at  T75  volts ;  with  potassium  chloride 
chlorine  at  2-1  volts. 

Preparation  of  Ammonium  Persulphate  from  Ammonium 
Sulphate — A  porous  pot  of  capacity  100  to  150  c.c.  serves  as 
the  anode  chamber.  This  is  surrounded  by  a  lead  spiral, 
through  which  cold  water  can  be  circulated.  A  piece  of 
copper  connecting  wire  is  soldered  on  to  the  lead  spiral  which 
forms  the  cathode.  The  anode  is  platinum  wire  spiral,  having 
a  surface  of  1  to  2  sq.  cms.  Fill  the  anode  chamber  with 
a  cold  saturated  solution  of  ammonium  sulphate,  the  space 
between  the  porous  pot  and  the  containing  beaker — i.e., 
cathode  chamber — being  filled  with  a  mixture  of  1  part  con- 
centrated sulphuric  acid  and  1  part  of  water,  by  volume. 
The  temperature  of  the  anode  chamber  should  be  kept 
between  10°  and  20°  by  circulating  iced  water  through  the 
lead  cathode  spiral.  The  anode  liquid  is  kept  saturated  with 
ammonium  sulphate  by  suspending  in  the  anode  chamber  a 
test-tube,  with  one  or  more  holes  at  the  bottom,  containing 
solid  ammonium  sulphate.  Pass  a  current  having  density  of 
500  to  1000  amperes  per  100  square  centimetres  at  the  anode, 
and  a  current  density  as  low  as  possible  at  the  cathode, 
thereby  saving  the  voltage,  and  excessive  evolution  of  heat. 
The  electrode  in  the  anode  chamber  should  dip  only  half-way 
into  the  liquid.  After  about  four  hours  stop  the  electrolysis 
and  filter  the  liquid  in  the  porous  pot.  The  crystals  thus 
obtained  are  dried  on  a  porous  plate.  The  filtrate  is  then  re- 
saturated  with  ammonium  sulphate,  returned  to  the  porous 
pot,  and  the  electrolysis  recommenced.  The  liquid  in  the 
cathode  gradually  becomes  neutralized  owing  to  the  migration 
of  the  sulphuric  acid  anions  out  of  it  and  the  ammonium  ions 
into  it.  Hence  from  time  to  time  the  acid  must  be  replaced. 
The  anode  liquid  becomes  poorer  in  ammonia,  and  accumulates 
free  acid.  Hence  after  every  two  operations  ammonia  should 
be  added  to  the  anode  liquid  (gradually  to  prevent  heating) 
until  the  acid  is  almost  neutralized.  At  the  first  operation  the 
separation  of  persulphate  is  small,  since  the  solution  has  first 
to  become  saturated  in  respect  to  persulphate.  In  later 
operations  the  deposit  commences  almost  immediately,  and  a 
good  yield  results.  The  current  efficiency  is  70  per  cent.,  and 


156 


ELECTROLYTIC  PREPARATIONS 


the  yield  60  per  cent.  It  is  essential  that  the  anode  should  be 
washed  with  water  and  heated  to  glowing  before  each  experi- 
ment. The  raw  product  contains  about  5  per  cent,  ammonium 
sulphate.  A  pure  specimen  can  be  obtained  (with  considerable 
loss)  by  making  quickly  a  saturated  solution  of  the  crude  salt 
with  water  at  50°  C.,  and  then  cooled  slowly  to  a  low  tempera- 
ture. Ammonium  persulphate  is  only  stable  when  perfectly 
dry.  The  purity  of  the  sample  may  be  tested  by  pouring  a 
solution  (freshly  made  up)  into  a  strongly  acid  solution  of 
ferrous  ammonium  sulphate  and  titra- 
ting the  excess  of  ferrous  salt  with 
potassium  permanganate.  It  must  be 
remembered  that  the  oxidation  by 
persulphate  takes  several  minutes  to 
accomplish  completely.  In  the  pre- 
paration of  persulphates,  hydrogen 
peroxide  and  its  derivatives  are  also 
formed  in  the  anode  chamber;  these 
can  be  determined  directly  by  perman- 
ganate. Hence,  to  follow  the  course 
of  electrolysis,  take  a  sample  of  the 
anode  liquid  titrate  with  permanganate, 
then  add  excess  of  acid  ferrous  am- 
monium sulphate.  The  first  titration 
gives  the  peroxide  content,  and  the  second  the  persulphate 
content.  Potassium  persulphate  may  be  similarly  prepared, 
but  the  method  is  not  quite  satisfactory.  In  small  quantity 
potassium  persulphate  can  be  easily  prepared  by  the  apparatus 
indicated  in  Fig.  71. 

A  wide  boiling-tube,  P,  contains  a  saturated  solution  of 
potassium  sulphate  in  sulphuric  acid,  of  specific  gravity 
1-2  to  1-3. 

The  anode,  A,  consists  of  a  platinum  wire,  a  large  portion  of 
which  is  surrounded  by  a  glass  tube,  into  which  the  platinum 
is  sealed.  The  wire  (which  must  be  ignited  before  use)  passes 
almost  to  the  bottom  of  the  boiling-tube.  A  wider  tube,  R, 
surrounds  the  anode  to  carry  away  the  oxygen  liberated  at 
the  anode,  without  stirring  up  the  liquid,  which  would  prevent 
concentration  at  the  anode.  The  cathode  consists  of  a  plati- 
num loop,  (7,  which  passes  outside  to  the  tube  R.  The  contents 
of  the  tube  are  kept  cool  by  immersing  the  whole  apparatus 
in  a  large  beaker  of  cold  water — use  a  current  density  of 


FIG-.  71 


PREPARATION  OF  AMMONIUM  PERSULPHATE     157 

100  amperes  per  100  sq.  cms.  at  the  anode,  utilizing 
a  current  of  1  to  2  amperes.  A  thick  deposit  of  potassium 
persulphate  will  form  at  the  bottom  of  the  vessel  after  ten 
minutes. 

The  formation  of  persulphates  at  the  anode  is  explained  by 
the  fact  that  in  concentrated  solutions  of  sulphates,  such  as, 
say,  ammonium  sulphate,  there  are  present  HS04  anions  as 
well  as  S04  anions,  and  the  greater  the  concentration  arid 
current  density  the  greater  the  extent  to  which  they  are 
discharged. 

The  discharged  anions  may  react  in  two  ways— 

/ONH4  X)NH4 

(1)  2S02<  +  H20  =  202S/  +0. 

X)—  X)H 

ONH4  X)NH4  NHXX 

o_    =02S/o  Q>0, 

High  current  density  favours  the  second  reaction,  hence  high 
current  densities  are  necessary  for  the  formation  of  persul- 
phates. The  above  graphic  formula  agrees  with  its  properties 
—  i.e.,  the  persulphates  behave  as  derivatives  of  hydrogen  per- 
oxide. Upon  warming  an  aqueous  solution  of  the  acid,  or  its 
salts,  oxygen  is  evolved. 

XONH4  NH40V  /ONH4 

02S<  >S02  =  2S02<  +0. 


X0 

A  low  temperature  is  therefore  necessary  for  their  prep- 
ation. 


aration 


CHAPTER  XIX 
PREPARATION  OF  COLLOIDS 

A  LARGE  number  of  substances  are  capable  of  apparently 
dissolving  in  water  to  form  what  may  be  termed  pseudo- 
solutions.  Such  pseudo-solutions  are  characterized  by  an  ex- 
tremely low  diffusive  power,  a  low  osmotic  pressure,  and  an 
inability  to  undergo  dialysis;  in  these  respects  they  differ 
from  true  solutions  of  crystalloids,  and  are  therefore  termed 
colloidal  solutions.  Such  colloidal  solutions  are  distinguished,, 
according  to  the  nature  of  the  solvent,  as  hydrosols  for  water 
as  a  solvent,  and  alcosols  when  alcohol  is  the  solvent.  If  the 
pseudo-dissolved  substance  is  separated  from  the  solvent,  it  is 
often  found  not  to  have  lost  the  power  of  again  passing  into 
colloidal  solution ;  such  are  termed  reversible  colloids.  On  the 
other  hand,  many  substances,  mainly  inorganic,  when 
separated  from  the  solution  do  not  possess  the  power  of  re- 
dissolving  again  except  by  some  special  process,  such  are 
termed  irreversible  colloids.  Solutions  of  irreversible  colloids 
can  be  obtained  by  Bredig's  method,  by  disintegrating  the 
substance  in  an  electric  arc  under  water,  by  double  decomposi- 
tion in  aqueous  solution,  preventing  precipitation  by  suitable 
means,  or  by  previously  imparting  to  the  solid  the  ability  to 
dissolve  by  treatment  with  small  quantities  of  acid  or  alkali. 
This  latter  method  is  known  as  peptization,  and  has  been 
employed  to  bring  metallic  oxides,  etc.,  into  a  plastic  con- 
dition for  the  formation  of  the  so-called  colloidal  electric  lamp 
filaments. 

Many  irreversible  colloids  separate  out  from  their  solutions 
as  voluminous  precipitates,  containing  a  large  amount  of  water ; 
such  are  known  as  hydrogels,  such  are  ferric  oxide,  aluminium 
oxide,  etc.  They  contain  far  more  water  than  is  required  for 
their  hydrates,  and  are  therefore  frequently  termed  oxide 
hydrogels. 

158 


COLLOIDS  159 

The  change  from  the  hydrosol  state  to  that  of  the  hydrogel 
can  be  very  easily  brought  about  by  the  addition  of  an 
electrolyte.  Many  colloidal  solutions  are  exceedingly  sensi- 
tive to  electrolytes,  hence  an  essential  condition  for  their 
preparation  is  the  entire  absence  of  an  electrolyte.  A  very 
characteristic  property  of  colloids  is  their  power  of  adsorption. 
Hence  different  dissolved  colloids  can  combine  together  to 
form  adsorption  compounds.  A  gold  hydrosol  is  exceedingly 
sensitive  to  electrolytes,  but  if  a  non-sensitive  colloid,  such  as 
gelatine,  is  added,  the  gold  solution  remains  stable  towards 
small  amounts  of  electrolyte.  This  would  seem  to  indicate 
that  some  kind  of  combination  had  taken  place  between  the 
two  dissolved  colloids.  Such  substances,  which  act  like 
gelatine,  are  known  as  protective  colloids. 

On  the  other  hand,  certain  colloids  have  the  property  of 
precipitating  one  another  out  of  solution.  Thus  arsenic 
sulphide  hydrosol  and  iron  oxide  hydrosol,  when  mixed  in  the 
correct  proportions,  are  precipitated  as  a  common  adsorption 
compound.  This  is  due  to  the  fact  that  colloids  carry  a  charge, 
and  in  this  case  the  charges  on  the  respective  hydrosols  are  of 
opposite  sign,  hence  they  neutralize,  and  precipitation  results. 
It  is  a  rule  that  two  such  colloids,  in  order  to  precipitate  each 
other,  must  have  charges  of  opposite  sign  when  referred  to  a 
common  solvent. 

The  fact  that  colloids  possess  a  charge  explains  why  they 
are  precipitated  by  electrolytes.  The  electrolyte  dissociates, 
giving  ions  of  opposite  charges,  and  that  which  is  opposite  in 
sign  to  that  of  the  pseudo-dissolved  substance  is  adsorbed, 
and  precipitation  results.  The  passage  of  a  colloidal  solution 
through  a  narrow  glass  tube  causes  the  precipitation  of  the 
colloid,  simply  because  the  charge  is  given  up  to  the  walls  of 
the  tube.  When  a  colloidal  solution  is  subjected  to  an 
electrical  potential,  the  colloid  "  wanders "  either  to  the 
anode  or  the  cathode,  according  to  its  charge.  Undoubtedly, 
then,  the  particles  do  carry  charges,  but  the  charges  are 
small  and  the  motion  slow,  and  the  number  of  moving 
particles  small  in  comparison  with  an  ordinary  electrolyte.  It 
is  also  uncertain  whether  the  particles  are  discharged  at  the 
poles. 

Preparation  of  Colloidal  Platinum  by  Bredig's  Method 
— Take  two  pieces  of  platinum  wire,  about  1  mm.  diameter 
and  10  to  15  cms.  long,  and  insulate  them  by  sealing  them 


160  PREPARATION  OF  COLLOIDS 

into  a  glass  tube  so  that  about  3  cms.  project.  Then  connect 
the  other  ends  of  the  wire  with  110-volt  lighting  circuit  by 
means  of  binding  screws,  these  junctions  being  insulated 
by  "  insulating  tape,"  or,  better,  by  a  wider  glass  tube  (see 
Fig.  72).  Insert  an  ammeter  and  a  resistance  in  the  circuit. 
Take  about  150  c.c.  of  distilled  water  in  a  glass  dish,  arid 
clamp  one  electrode  so  that  it  dips  below  the  surface  of 
the  water.  Take  the  other  in  the  hand  and  touch  the  first 
one,  and  then  remove  it  a  short  distance,  so  as  to  maintain 
a  small  arc  under  water.  A  current  of  6  to  10  amperes 
should  be  used,  this  being  regulated  by  the  resistance.  Of 
course,  care  must  be  taken  to  see  that  the  wiring  will 
take  such  a  current.  It  is  not  usually  possible  to  maintain 
an  arc  for  any  length  of  time,  so  that  when  the  arc  breaks 


FIG.  72 

it  must  be  restarted  by  bringing  the  electrodes  into  con- 
tact again.  This  process  is  repeated  until  the  solution 
becomes  almost  opaque  or  very  hot.  The  solution  thus 
obtained  contains  a  considerable  amount  of  coarse  platinum 
powder.  This  is  removed  by  filtering  the  solution.  The 
filtrate  then  contains  colloidal  platinum. 
Test  the  colloidal  solution  as  follows  : 

1.  Take  a  few  cubic  centimetres  in  a  test-tube,  and  add  a 
drop  or  two  of  an  electrolyte    (say   KC1  solution) ;   after   a 
time  the  colloid  metal  separates  out. 

2.  To  a  few  cubic  centimetres  of  a  dilute  solution  of  hydro- 
gen-peroxide   add   a    few   drops   of  the    colloidal    solution. 
Oxygen    is   evolved,    due    to    the    catalytic   action   of    the 
platinum. 

Preparation    of    Colloidal    Antimony    Sulphide— Prepare 
100  c.c.  of  a  1  per  cent,  solution  of  tartar  emetic,  and  place 


COLLOIDAL  ANTIMONY  SULPHIDE  .  161 

it  in  a  dropping  funnel,  and  allow  it  to  drop,  drop  by  drop, 
into  100  c.c.  hydrogen  sulphide  water,  through  which  a 
moderately  rapid  stream  of  hydrogen  sulphide  is  passing. 
Under  these  conditions  no  precipitate  of  antimony  sulphide 
should  be  formed,  but  the  antimony  sulphide  should  remain 
in  colloidal  suspension  as  a  deep  orange-coloured  pseudo- 
solution,  which  is  perfectly  clear  when  seen  by  transmitted 
light.  The  excess  of  hydrogen  sulphide  must  now  be 
removed  by  passing  through  the  solution  of  pure  hydrogen. 
The  solution  thus  obtained  is  now  dialyzed.  This  may  be 
conveniently  done  by  stretching  a  sheet  of  parchment  over  a 
wooden  hoop,  thus  forming  a  sort  of  tambourine,  and  floating 
this  in  a  basin  of  water  (see  Fig.  73). 
The  solution  is  placed  inside  the 
drum,  and  the  salts  present  in  solu- 
tion  gradually  diffuse  through  the 
orange-coloured  material  remaining 
on  the  parchment.  Fresh  quantities 
of  distilled  water  are  added  to  the 
colloid  in  the  drum  every  three  or 
four  hours  the  first  day,  and  later 
every  twelve  hours  for  four  days, 
after  which  the  colloidal  solution  FIG.  73 

will    be    free    from    foreign     salts. 

The  orange    solution    may   then  be  transferred  to  a    clean 
beaker. 

Experiments  with  Colloidal  Antimony  Sulphide — Prepare 
approximately  normal  solutions  of  potassium  chloride,  barium 
chloride,  and  aluminium  chloride.  Take  three  separate 
portions  of  10  c.c.  each  of  the  colloidal  solution,  and  to  each 
portion  add  one  of  the  above  standard  solutions  from  a 
burette,  and  determine  the  amount  of  each  of  the  above 
electrolytes,  which  will  just  completely  precipitate  the  anti- 
mony from  the  solution.  This  should  be  done  roughly  at 
firs't,  allowing  the  precipitate  to  settle  after  each  addition, 
and  noting  the  effect  of  the  next  addition  in  the  supernatant 
liquid,  which  should  gradually  become  colourless.  The  largest 
amount  of  electrolyte  required  will  be  in  case  of  potassium 
chloride,  and  the  smallest  in  the  case  of  aluminium  chloride. 
The  precipitating  power  depending  for  this  class  of  colloid  on 
the  valency  of  the  cation — i.e.,  on  its  electrical  charge. 
11 


162  PREPARATION  OF  COLLOIDS 

Preparation  of  Colloidal  Gold  Solution  by  Donau's  Method — 
Dissolve  0-25  gram  of  crystallized  HAuCl^SHgO  in  500  c.c.  of 
distilled  water.  Pass  through  this  solution  a  slow  stream  of 
carbon  monoxide,  prepared  from  oxalic  acid  and  strong 
sulphuric  acid,  passing  the  gas  first  through  a  solution  of 
potassium  hydroxide  to  remove  the  carbon  dioxide.  There  is 
produced  first  a  violet,  then  a  reddish-violet,  followed  by  a 
deep  red  coloration.  Stop  the  reaction  at  this  point.  Pre- 
serve the  solution  for  later  experiments. 

Preparation  of  Colloidal  Stannic  Oxide — To  5  c.c.  of  tin 
tetra  chloride  add  150  c.c.  of  distilled  water,  thus  hydro- 
lyzing  it.  Add  this  solution  to  500  c.c.  of  distilled  water,  to 
which  a  few  drops  of  ammonia  have  been  added.  Dialyze 
this  solution  for  five  days,  changing  the  outside  water,  about 
three  times  a  day  until  it  shows  no  test  for  chlorides.  It  is 
quite  probable  that  the  hydrogel  may  to  some  extent  result. 
The  contents  of  the  dialyzer  are  transferred  to  a  beaker,  and 
the  gel.  peptised  by  the  addition  of  three  or  four  drops  of 
ammonia.  After  a  time  the  jelly  will  completely  dissappear, 
leaving  a  perfectly  clear  hydrosol. 

A  pseudo-solution  of  zircon  oxide  may  be  similarly  pre- 
pared by  dialyzing  for  five  days  a  15  per  cent,  solution  of 
zircon  nitrate. 

The  ferric  oxide  hydrosol  may  be  prepared  from  dilute 
ferric  chloride  similarly. 

Experiments — (1)  To  2  c.c.  of  the  colloidal  gold  solution 
add  2  c.c.  of  the  stannic  oxide  hydrosol ;  no  change  occurs. 
Now  add  a  little  ammonium  chloride  solution ;  a  beautiful 
deep  reddish  purple  precipitate  is  formed,  which  has  the 
characteristic  property  of  being  soluble  in  ammonia.  In  this 
experiment  we  have  synthesized  the  Purple  of  Cassius. 

(2)  Take  75  c.c.  of  a  boiling  colloidal  gold  solution  and 
add   15    c.c.  of  boiling  zircon  hydrosol  solution  ;  a  zircon- 
gold-purple  precipitate  results  in  this  case  without  the  addi- 
tion of  an  electrolyte.     The  precipitation  takes  place  slowly 
in  the  cold. 

(3)  Take  10  c.c.  of  the  colloidal  gold  solution  and  add  a 
few  drops  of  hydrochloric  acid ;  a  blue  coloration  first  results, 
followed  by  a  deposit  of  the  metal.     Take  a  further  10  c.c. 
of  the  gold  hydrosol  solution  and  add  1  drop  of  a  2  per  cent, 
solution  of  gelatine,  and  again  add  a  little  hydrochloric  acid. 
In  this  case  there  is  neither  change  of  colour  nor  a  deposit 
of  the  metal.     Here  we  have  an  example  of  a  protective  colloid. 


APPENDIX 

TABLE  OF  RELIABLE  MELTING  AND  BOILING- 
POINTS 


Liquid  Hydrogen           ...............  _  253° 

Liquid  Oxygen  ...         ...         ...         ...  —182° 

Freezing  Mercury          ...         ...         ...  _  390 

Melting  Ice         ...         ...         ...  0° 

Boiling-point  of  Aniline  at  760  mm.  pressure            ...  184° 

11          ,,          Naphthalene  ............  220° 

,,           „          Diphenylamine           .........  302° 

,i          „          Sulphur           ............  445° 

Melting-point  of  Tin     ...............  232° 

„           ,,          Zinc   ...............  419° 

>,           „          Antimony      ............  632° 

»           »          Aluminium    ...         ...         ...         ...  657° 

i)           „          Sodium  Chloride      .........  800° 

»           „          Silver  (in  air)            .........  955° 

ii           ,>          Silver  (in  reducing  atmosphere)     ...  962° 

Gold  ...                     .........  1064° 

»           ,,          Copper  (in  air)         .........  1062° 

»           „          Potassium  Sulphate..           ......  1070° 

ii           «          Copper  (in  reducing  atmosphere)  ...  1084° 

„          Nickel           ............  1427° 

>,           „          Pure  Iron      ............  1503° 

,,           „          Palladium     ...........  1545° 

„           „          Platinum       ............  1750° 

Boiling-point  at  760  mm.  pressure  of  Magnesium     ...  1120° 

»i           »             ,,                 „             Antimony       ...  1440° 

n           5>             „                 „             Lead    ......  1525° 

j>           »             „                 ,,             Aluminium     ...  1800° 

>»           »             »                 „             Manganese      ...  1900 


...  ° 

„ 


Silver 1955° 

„  „  Chromium      ...  2200° 

Tin      2270° 

Copper  ...  2310° 

Iron 2450° 

163 


164 


APPENDIX 


DENSITY  OF  WATER 


Temperature 

Density 

Temperature 

Density 

0° 

0-99987 

21° 

0-99802 

1° 

0-99993 

22° 

0-99779 

2° 

0-99997 

23° 

0-99756 

3° 

0-99999 

24° 

0-99732 

4° 

1-00000 

25° 

0-99707 

5° 

0  99999 

26° 

0-99681 

6° 

0-99996 

27° 

0-99654 

7° 

0-99993 

28° 

0-99626 

8° 

0-99988 

29° 

0-99597 

9° 

0-99981 

30° 

0-99567 

10° 

0-99973 

31° 

0-99537 

11° 

0-99963 

32° 

0-99505 

l'2° 

0-99953 

33° 

0-99473 

13° 

099940 

34° 

0-99440 

14° 

0-99927 

35° 

0-99406 

15° 

0-99913 

40° 

0-99224 

16° 

0-99897 

50° 

0  98807 

17° 

0-99880 

60° 

0-98324 

18° 

0-99862 

70° 

0-97781 

19° 

0-99843 

80° 

0  97183 

20° 

0-99823 

90° 

0-96534 

VAPOUR  PRESSURES  OF  WATER 


Temperature 

Vapour  Pressures 

Temperature 

Vapour  Pressures 

Mm. 

Mm. 

4° 

6-1 

19° 

16-5 

5° 

6-5 

20° 

17-5 

6° 

7-0 

21° 

18-7 

7° 

7-5 

22° 

19  8 

8° 

8-0 

23° 

21-1 

9° 

8-6 

24° 

22-4 

10° 

9-2 

25° 

23-8 

11° 

9-8 

26° 

25-2 

12° 

105 

27° 

26-7 

13° 

11-2 

28° 

28-4 

14° 

12-0 

29° 

30-1 

15° 

12-8 

30° 

31-8 

16° 

136 

31° 

33-7 

17° 

14-5 

32° 

35-7 

18° 

15-5 

33° 

37-7 

APPENDIX 


165 


VISCOSITY  AND  SURFACE  TENSION  OF  WATER 


Tempera- 
ture 

Viscosity 

Surface 
Tension 

Tempera- 
ture 

Viscosity 

Surface 
Tension 

10° 



74-05 

35° 

0-00724 



15° 



73-26 

35° 



7029 

15° 

0-01142 



40° 



69-54 

20° 

— 

72-53 

40° 

0-00657 



20° 

0-01006 

— 

45° 

— 

68-6 

25° 

0-008926 



45° 

0-00600 



25° 

71-78 

50° 

— 

67-8 

30° 



71-03 

50° 

0-005500 



30° 

0-00800 

— 

1 

PHYSICAL  DATA  FOR  BENZENE 


Temperature                   Density 

Viscosity              Surface  Tension 

0°                         0-9006 

11-4°                                                                                        28-83 

14-8° 

— 

0007038                        — 

20° 

0-8790 

30-8° 

0-005522 

31-2° 

26-68 

40° 

0-8576 

—                             — 

46-9° 



0-004435                        — 

55-1° 

— 

2353 

60° 

0-8357 



— 

68-5° 





21-70 

70° 

0-8247 



— 

78-3° 

— 

— 

20-51 

78-8° 

~ 

0-003177 

^~" 

DENSITY  OF  PURE  ALCOHOL 


Temperature 

Density 

Temperature 

Density 

10° 
20° 
30° 

0-7979 
0-7894 
0-7810 

40° 
50° 

0-7722 
0-7633 

16(5 


APPENDIX 


DEGREES  OF  IONIZATION  OF  SOME 
ELECTROLYTES  AT  18° 


Electrolytes 

N 

n 
10 

Electrolytes 

N 

n 

To 

CuS04 

0-21 

0-38 

KI 

0-79 

0-86 

AgNOs 

0-58 

0-81 

KN03 

063 

0-83 

ZnS04 

0-23 

0-39 

NaCl 

0-68 

0-84 

KC1 

076 

0-86 

HC1 

071 

0-92 

KBr 

— 

0-86 

EQUIVALENT  CONDUCTIVITY  OF  INFINITE 
DILUTION 


Tempera- 
tures 

Electrolytes 

Conduc- 
tivity 

Tempera- 
tures 

Electrolytes 

Conduc- 
tivity 

18° 

NaOl 

108-99 

18° 

KCNS 

121-30 

18° 

NaNO, 

105-33 

18° 

KC10, 

11970 

18° 

KC1 

130-10 

18° 

AgNOg 

115-80 

18° 

KBr           1    132-30 

25° 

Acetic  Acid 

389 

18° 

oroa 

126-50 

25° 

Benzoic  Acid 

381 

DISCHARGE  VOLTAGES  OF  DIFFERENT  IONS 
FROM  AQUEOUS  SOLUTIONS 

On  reversing  the  signs,  the  values  represent  the  solution 
tendency. 

(a)  Cation  discharge  points. 


Cation 

Volts 

Cation 

Volts 

K' 

-2-92+*  (0-058  log  10C) 

Ni" 

+  0-06  +  -(0-058  log  ,0C) 

Na' 

--2-52  +  , 

Pb" 

+  0-16   +, 

Mg" 

-1-27  +  , 

Sn" 

+  0-18   +, 

Zn" 

-0-48  +  , 

H' 

+  0-277+, 

Fe" 

-0-15  +  , 

Cu" 

-f-0-62  +  , 

Cd" 

-0-12  +  , 

Ag' 

+  1-08   +, 

Tl' 

-0-04  +  , 

Hg" 

+  1-14   +, 

CO" 

-0-01+, 

Au' 

+  1*78  +, 

APPENDIX 

(b)  Anion  discharge  points. 


167 


40H'( — X>2+2HS0) 

Br' 

Cl' 


-0-28  +  ^(0-058  log  10C) 

0-69  + 
0-82  + 
1-36  + 
1-63  + 

2-18  + 


C  =  Ionic  concentration  at  25°. 
n  =  Valency. 

SPECIFIC  HEATS  AND  ELECTRICAL  RESISTANCES  AT  0° 


Specific  Heat 

Specific  Resistance 

Aluminium 
Iron    .  .  . 
Copper 
Nickel 
Platinum 
Silver 
Mercury 
Glass 

•• 

0-22 

0-11 

0-093 
0-11 
0-032 
0-056 
0-0332 
0*19 

0-028xlO-4 
0-99   -0-15x10-* 
0-Ol7xlO-4 
0-08   -0-llxlO-4 
0-108-0-11  xlO-4 
0-016x10-4 
0-958x10-4 
1-0      xlO-15 

Graphite 
Retort  carboi 

i 

. 

•• 

0-155 
0-165 

14-3      xlO-4 
49-0      xlO-* 

LIQUID  PLATINUM 

Moisten  0-3  gram  of  platinic  chloride  with  cone.  HC1,  and 
mix  with  1  c.c.  of  cone,  boric  acid  solution.  Dissolve  in  alcohol 
and  a  Id  1  c.c.  of  French  turpentine,  and  2  c.c.  of  oil  of 
lavender. 

NERNST  LIQUID  RESISTANCE 

The  Nernst  liquid  resistance,  suitable  for  conductivity  work, 
consists  of  121  grams  of  mannite,  41  grams  of  boric  acid  and 
0-06  gram  KC1  in  a  litre  of  aqueous  solution.  K  =  0-00097  at 
18°,  and  temperature  coefficient  is  exceedingly  small. 


TABLOID  PRESS 

A  suitable  form  of  press  for  making  compressed  tabloids,  as 
required  for  combustion  experiments,  etc.,  is  as  shown  in 
Fig.  73.  It  consists  of  a  mould,  M,  the  two  halves  being 


168 


APPENDIX 


joined  by  a  hinge  on  one  side  and  secured  by  a  winged  nut 
on  the  other.  The  substance  of  which  a  tabloid  is  required  is 
placed  in  the  mould  (in  the  case  of  hard  substances  like  coal 
they  should  be  finely  powdered)  and  a  plunger  inserted.  The 
mould  is  then  placed  in  the  screw  press,  as  indicated  in  Fig.  74, 


FIG.  74 

and  the  screw  turned  as  far  as  possible,  thus  exerting  great 
pressure  on  the  substance.  The  pressure  is  then  relieved, 
and  then  by  undoing  the  winged  nut  the  mould  can  be 
opened  and  the  tabloid  removed.  In  order  to  make  a  tabloid 
successfully,  the  groove  of  the  mould  must  be  perfectly  clean, 
and  kept  as  smooth  as  possible. 


APPENDIX 


169 


DETERMINATION  OF  MOLECULAR  WEIGHTS  BY  THE 
ELEVATION  OF  BOILING-POINT  AND  DEPRES- 
SION OF  THE  FREEZING-POINTS  (BECKMANN'S 
METHOD) 

1.  VALUES  OF  K  FOR  BOILING-POINT  METHOD 


Solvent 

Boiling-Poiut 

K 

Ether 

34-9° 

2110 

Carbon  disulphide    .. 

46-2° 

2370 

Acetone 

56-3° 

1670 

Chloroform    ... 

61-2° 

3660 

Ethyl  acetate 

74-6° 

2610 

Ethyl  alcohol           

78'3° 

1150 

Benzene 

80'3° 

2670 

Water            ...                    

100-0° 

520 

Acetic  acid    ... 

118-1° 

2530 

2.  VALUES  OF  K  FOR  FREEZING  POINT  METHOD 


Solvent 

Freezing-Point 

K 

Water 

0° 

18GO 

Acetic  acid     ... 
Benzene 

17° 
5'5° 

3860 
5000 

LATENT  HEATS 


Solvent 

Vaporization 

Fusion 

Water                                                          .  . 

535-9° 

79-1° 

Acetic  acid 

43-1° 

Benzene 

92-9° 

30-1° 

Ether  
Acetone 

0  90° 
125-3° 

Ethyl  alcohol            

215-0° 

— 

170 


APPENDIX 


VALUES  OF  K  (LANDSBERGER'S  METHOD) 


Solvent 

K 

Solvent 

K 

Alcohol 
Ether    '.. 
Water  

1560 
8030 
540 

Acetone 
Chloroform 
Benzene 

2220 
2600 
3280 

Note — The  values  of  K  in  Beckmann's  Method  are  for  1  gram  of 
solvent,  whereas  those  for  Landsberger's  Method  are  for  1  c.c.  of  solvent. 
In  the  former  case  the  weight  of  the  solvent  is  known,  and  the  latter  case 
the  volume. 


VALUES  OF  /tw  at  25°  C.  (SEE  CONDUCTIVITY) 


Acid 

Moo 

K=100  * 

Acetic  acid 

389 

1'8    xlO-3 

Succinic  acid 
Benzoic  acid 

381 
381 

6-65xlO-3 
6-0    xlO-3 

Mandelic  acid 

378 

4-17  xlO-2 

DENSITY  OF  ACETONE 

Density  (15°/4°)  =  07971 


APPENDIX  171 

INTERNATIONAL  ATOMIC  WEIGHTS,  1914 


Element 

Symbol 

Atomic 
Weight 

Element 

Symbol 

Atomic 
Weight 

Aluminium     ... 

Al 

27-1 

Neon    ... 

Ne 

20-2 

Antimony 

Pb 

120-2 

Nickel 

Ni 

58-68 

Argon  ... 

A 

39-88 

Niobium 

Nb 

93-5 

Arsenic 

As 

74-96 

Niton  

Nt  . 

224-4 

Barium 

Ba 

137-37 

Nitrogen 

N 

14-01 

Beryllium 

Be 

9-1 

Osmium 

Os 

190-9 

Bismuth 

Bi 

208-0 

Oxygen 

0 

16-0 

Boron  ... 

B 

11-0 

Palladium 

Pd 

106-7 

Bromine 

Br 

79-92 

Phosphorus     ... 

P 

31-04 

Cadmium 

Cd 

112-40 

Platinum 

Ft 

195-2 

Caesium 

Cs 

132-81 

Potassium 

K 

39-10 

Calcium 

Ca 

40-07 

Praseodymium 

Pr 

140-6 

Carbon 

C 

12-0 

Radium 

Ra 

226-4 

Cerium 

Ce 

140-25 

Rhodium 

Rh 

102-9 

Chlorine 

Cl 

35*46 

Rubidium 

Rb 

88-45 

Chromium 

Cr 

52-0 

Ruthenium 

Ru 

101-7 

Cobalt  

Co 

58-97 

Samarium 

Sa 

150-4 

Copper 

Cu 

63-57 

Scandium 

Sc 

44-1 

Dysprosium    .  .  . 

Dy 

162-5 

Selenium 

Se 

79-2 

Erbium 

Er 

167-7 

Silicon 

Si 

28-3 

Europium 

Eu 

152-0 

Silver  

Ag 

107-88 

Fluorine 

F 

19-0 

Sodium 

Na 

23-0 

Gadolinium    ... 

Gd 

157-3 

Strontium 

Sr 

87-68 

Gallium 

Ga 

69-9 

Sulphur 

S 

32-07 

Germanium     .  .  . 

Ge 

72-5 

Tantalum 

Ta 

181-5 

Gold     

Au 

197-2 

Tellurium 

Te 

127-5 

Helium 

He 

3-99 

Terbium 

Tb 

159-2 

Holmium 

Ho 

163-5 

Thallium 

Tl 

204-0 

Hydrogen 

H 

1-008 

Thorium 

Th 

232-4 

Indium 

In 

114-8 

Thulium 

Tm 

168-5 

Iodine  

I 

126-92 

Tin       

Sn 

119-0 

Iron 

Fe 

55-84 

Titanium 

Ti 

48-1 

Krypton 

Kr 

88-92 

Tungsten 

W 

184-0 

Lanthanum     .  . 

La 

139-0 

Uranium 

U 

238-5 

Lead     

Pb 

207-10 

Vanadium 

V 

51-0 

Lithium 

Li 

6-94 

Xenon  ... 

Xe 

130-2 

Lutecium 

Lu 

1740 

Ytterbium  (Neo- 

Magnesium     .  .  . 

Mg 

24-32 

ytterbium)  ... 

Yb 

172-0 

Manganese      ... 

Mn 

54-93 

Yttrium 

Y 

89-0 

Mercury 

Hg 

200-6 

Zinc     

Zn 

65-37 

Molybdenum  ,  .  . 

Mo 

96-0 

Zirconium 

Zr  ' 

90-6 

Neodymium   ... 

Nd 

144-3 

172 


LOGARITHMS 


Num- 
ber 

0 

1 

2 

3 

4     5 

6 

7 

8 

9  (I  1  2  3 

456 

789 

10 

0000 

0043 

0086 

0128 

0170 

02120253 

0294 

0334 

0374 

j  4     8  12 

17  21  25 

29  33  37 

11 

0414 

0453 

0492 

0531 

0569 

0607  0645 

0682 

0719 

0755 

4     8  11 

15  19  23 

26  30  34 

12 

0792 

0828 

0864 

0899 

0934 

09691004 

1038J1072 

1106 

3     7  10 

14  17  21 

24  28  31 

13 

1139 

1173 

1206 

1239 

1271 

1303 

1335 

1367 

1399 

1430 

3     6  10 

13  16  19 

23  26  29 

14 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

1703 

1732 

369 

12  15  18 

21  24  27 

15 

1761 

17901818 

1847 

1875 

19031931 

1959 

1987 

2014 

368 

11  14  17 

20  22  25 

16 

2041 

2068  2095 

2122 

2148 

21752201 

2227 

2253 

2279 

358 

11  13  1618  21  24 

17 

2304 

2330  2355 

2380 

2405 

2430]2455 

2480 

2504 

2529 

257 

10  12  15  17  20  22 

18 

2553 

2577|2601 

2625 

2648 

2672 

2695 

2718 

2742 

2765 

2     5     7 

9  12  14  16  19  21 

19 

2788 

2810 

2833 

2856 

2878 

2900 

2923 

2945 

2967 

2989 

247 

9  11  1316  18  20 

20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

246 

8  11  13 

15  17  19 

21 

3222 

3243 

3263 

3284 

3304 

3324 

3345 

3365 

3385 

3404 

246 

8  10  12 

14  16  18 

22 

3424 

3444 

3464 

3483 

3502 

3522 

3541 

3560 

3579 

3598 

246 

8  10  12 

14  15  17 

23 

3617 

3636 

3655 

3674 

3692 

3711 

3729 

3747 

3766 

3784 

246 

7     9  11 

13  15  17 

24 

3802 

3820 

3838 

3856 

3874 

3892 

3909 

3927 

3945 

3962 

2     4     5 

7     9  11 

12  14  16 

25 

3979 

3997 

4014 

4031 

4048 

4065 

4082 

4099 

4116 

4133 

235 

7     9  10 

12  14  15 

26 

4150 

4166 

4183 

4200 

4216 

4232 

4249 

4265 

4281 

4298 

235 

7     8  10 

11  13  15 

27 

4314 

4330 

4346 

4362 

4378 

4393 

4409 

4425 

4440 

4456 

235 

689 

11   13  14 

28 

4472 

4487  4502 

4518 

4533 

4548 

4564 

4579 

4594 

4609 

235 

689 

11   12  14 

29 

4624 

4639  4654  4669 

4683 

4698 

4713 

4728 

4742 

4757 

1     3     4 

679 

10  12  13 

30 

4771 

4786|4800 

4814 

4829  4843 

4857 

4871 

4886 

4900 

1     3     4 

679 

10  11  13 

31 

4914 

4928 

4942 

4955 

4969  4983 

4997 

5011 

5024 

5038 

1     3     4 

678 

10  11  12 

32 

5051 

5065 

5079 

5092 

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534755117568 

235 

7     9  1012  14  16 

•88 

7586 

7603|7621  7638 

7656 

7674  7691 

7097727)7745 

245 

7     9  11  12  14  16 

89 

7762 

778017798.7816 

834 

7852;7870 

889  7907 

7925 

245 

7     9  11J13  14  16 

•90 

7943 

7962  7980 

7998 

8017  8035  8054 

8072;8091 

8110 

2     4     67     9  11 

13  15  17 

•91 

8128 

81478166 

8185 

8204J8222  8241 

8260  8279 

8299 

2     4     68     9  11 

13  15  17 

'92 

8318 

8337!8356 

8375 

8395J8414J8433 

453 

8472 

8492 

2     4     6    8  10  11 

14  15  17 

93 

8511 

8531  8551 

8570 

8590|8610|8630 

650 

8670 

8690 

2     4     6    8  10  12 

14  16  18 

94 

8710 

8730  8750 

8770 

790  8810 

8831 

851 

8872 

8892 

2     4     6    8  10  12 

14  16  18 

•95 

8913 

8933  8954 

8974 

9959016 

9036 

057 

9078 

9099 

2     4     6    8  10  12 

15  17  19 

•96 
97 

9120 
9333 

91419162 
93549376 

9183 
9397 

20492261 
4199441 

9247 
9462 

2689290 
484  9506 

9311 
9528 

2     4     6    8  11  13 

2     4     7|  9  11  13 

15  17  19 

15  17  20 

•98 

9550 

9572  9594 

9616 

638 

9661 

9683 

7059727 

9750 

2    4     7    9  11  13 

16  18  20 

99 

9772 

9795!9817 

9840 

86398869908 

931|9944 

9977 

2     5     7-  9  11  14 

16  18  20 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

123 

456789 

INDEX 


ABNORMAL  molecular  weight,  33 

Affinity  constant,  105 

Alcohol,  density  of,  165 

Ammonium  persulphate,  prepara- 
tion of,  155 

Aniline,  preparation  of,  from  nitro- 
benzene, 152 

Antimony  sulphide,  colloidal,  161 

Association  factor  for  liquids,  19,  34 

Azobenzene,  preparation  of,  from 
nitrobenzene,  153 

Balance,  ix 

determination  of  zero,  ix 
of  sensibility,  x 

Beckmann  thermometer,  23 

Benzene,  physical  data  for,  165 

Bimolecular  reactions,  141 

Boiling-point  determination,  24 

Beckmann's  apparatus,  26 
electrical  apparatus,  28 
Landsberger's  method,  29 

Boiling-points,  standard,  163 

Bomb  calorimeter,  80,  81 

Cadmium  cell,  110 
Callibration  of  bridge  wire,  96 
Calomel  electrode,  119 
Calorimeter,  74 

Cane  sugar,  specific  rotation  of,  58 
purity  of  a  sample  of,  59 
Capillarity,  18 
Capillary  electrometer,  113 
Cell  constant,  100 
Cells,  concentration,  126 

gas,  131 

Colloids,  preparation  of,  158 
Combustion,  heat  of,  79-86 
Conductivity,  equivalent,  92,  166 

molecular,  92,  103 

of  electrolytes,  92 


Conductivity    of    KC1    solutions 

101 

of  water  98 
specific,  92 
vessel,  94 
Copper  voltameter,  122 

electrolytic  estimation  of,  145 
Cryoscopic  method  for  determina- 
tion of  molecular  weight,  31 

Decomposition,  potential  of  electro- 
lytes, 147 
Density  of  gases  and  vapours,  6-10 

of  liquids,  10-12 

of  water,  10,  164 
Deposition  of  metals,  147 
Depression  of  the  freezing-point,  31 
Dialysis,  161 
Dilatometer,  37 

Dilatometric  method  for  the  deter- 
mination of  transition-points,  38 
Dissociation  constant  of  acids,  104 
Distribution  coefficient,  71 

of   a  substance  between    two 
non-miscible  solvents,  72 

Electro  analysis,  144 
Electrode  calomel,  119 
hydrogen,  131 
potential    measurement,    124, 

133 

potentials,  117 

Electrodes  of  platinum  on  glass,  133 
preparation  of,  106,  122 
testing  uniformity  of,  123 
Electrolytic  preparations,  151 
Electrometer,  capillary,  113 
Electromotive  force,  107 

influence  of  concentration 

on, 126 
measurement  of,  108 


176 


INDEX 


177 


Electromotive  force,  standard  of, 

110 
Elevation  of  the  boiling-point,  24 

Freezing-point  apparatus,  31 

method  for  determining  molec- 
ular weight,  32 

Gas  cells,  131 
Geisler  tube,  68 
Gold,  colloidal,  162 

Heat  of  combustion,  79  86 
of  dilution,  79 
of  hydration,  78 
of  neutralization,  74 
of  precipitation,  79 
of  solution,  78 
Hess's  law,  74 

Hydrochloric  acid,  strength  of  solu- 
tion by  conductivity  measure- 
ment, 106 

Hydrogen  spectrum,  68 
Hydrolysis  of  esters  by  acids,  138 
by  alkali,  142 

Inversion  of  cane  sugar,  velocity  of, 

140 

lodoform,  preparation  of,  153 
lonization  constant,  104 
degree  of,  103,  166 

Key,  Morse,  114 
tapping,  114 

Landberger- Walker  apparatus,  29 
Lead,    electrolytic    estimation    of, 

147 

Liquid  platinum,  167 
Logarithms,  172 

Mapping  of  spectra,  66 

Measuring-bridge,  95 
calibration  of,  96 

Mercury  pipette,  4 

Molecular  volume,  12 

Molecular  weight,  abnormal,  33 

Molecular  weight,  determination  of : 
by  boiling-point  method,  24-30 
by  distribution  method,  73 
by  freezing-point  method,  31 
by  vapour  density  method,  10 
12 


Nernst  liquid  resistance,  197 

Neutralization  -  point,  determina- 
tion of,  by  conductivity  method, 
106 

Nickel,  electrolytic  estimation  of, 
147 

Nitrates,  electrolytic  estimation  of, 
148 

Nitric  acid,  electrolytic  estimation 
of,  148 

Observation   tube   for  polarimeter, 

59 

Ohm's  law,  91 
Order  of  reaction,  143 
Osmotic  pressure,  41,  44 

measurement,  43 

Oxidation  and  reduction  cells,  134 
potential,  measurement  of,  135 

Partition  coefficient,  71 
Persulphates.  157 

preparation  of,  155 
Pipette,  mercury,  4 
Platinizing  electrodes,  1^6 
Platinum,  colloidal,  159 

solution,  167 
Polarimeter,  56,  61 
adjustment,  57 
measurements,  58 
Potassium  persulphate,  preparation 

of,  156 
Potential,  electrode,  measurements 

124,  133 
Pyknometer,  10 

Reaction  of  first  order,  137 

of  second  order,  141 

order  of  a,  143 

Reduction  of  aromatic  nitro  com- 
pounds, 151 

potential,  measurement  of,  136 
Refractive  index,  46 

of  a  liquid,  measurement 

of,  49 
Refractivity,  atomic,  52 

molecular,  49 

of  substance  in  solution,  53 

specific,  49 

Refractometer,  Pulfrich's,  48,  49 
Resistance,  specific,  92 
Rotation,  specific,  55 


178 


PRACTICAL  PHYSICAL  CHEMISTRY 


Rotation  of  plane  of  polarization, 
55 

Saponification  of  esters  by  acids, 

138 

by  alkalis,  142 
Semipermeable  membrane,  42 
Silver,  electrolytic  estimation  of, 

148 

Solubility,  determination  of,  21 
method  of  determining  transi- 
tion points,  40 
Solvents,  associating,  71 

dissociating,  71 
Spectra,  mapping,  66 

measurements,     reduction     to 

absolute  scale,  69 
Spectroscope,  64 

adjustment  of,  65 
Spectrum  analysis,  62 
Standard  cell,  110 
Stannic  oxide,  colloidal,  162 
Stirrers,  5 
Surface  energy,  molecular,  19 

ethyl  alcohol,  20 
tension,  18 
Suspended  transformation,  37 

Tabloid  press,  167 
Temperature,  regulation  of,  1 
Tensimeter,  39 
Thermo-chemistry,  74 
Thermometer,  Beckmann's,  23 

setting  of,  23 

Thermometric  method  for  the  deter- 
mination of  transition -points,  36 


Thermo-regulator,  1 

filling  of,  3 

for  low  temperatures,  4 
Thermostats,  1 
Transition -points,  determination  of, 

35 
Transport  numbers,  87 

Unimolecular  reactions,  137 

Vapour  density,  determination  of, 

6-10 
pressure  of  water,  164 

method  determination   of 

transition-points,  39 
Velocity  of  reactions,  137 
Viscosity,  15 

coefficient  of,  15,  17 
influence  of  temperature  on,  1 7 
of  benzene,  17 
relative,  18 
Voltameter,  copper,  122 

Water,  density  of,  164 

vapour  pressure  of,  164 
viscosity  and  surface  tension 

of,  165 
Wave  lengths,    determination    of, 

70 

Weighing,  x 

Weights,  calibration  of,  xi 
Weston's  cell,  110 

E.M.F.  of,  116 
preparation  of,  111 


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